feat(central-ui): InstanceTreeBuilder — area/instance forest for the instance picker

Task 1 of the Instance Picker plan (docs/plans/2026-09-08-instance-picker.md).
Pure, DI-free builder that nests a site's areas by ParentAreaId and hangs each
area's instances beneath it, mirroring Topology's ordering (child areas first,
then that level's instances; OrdinalIgnoreCase sorts) with unparented instances
at the root after the root areas. Orphaned areas become roots, a case-insensitive
filter keeps matching instances plus their ancestors and drops empty branches,
and a ParentAreaId cycle can never recurse forever.

Claude-Session: https://claude.ai/code/session_01NcMG6xXdsJbmD2wYAgkK29

src/ZB.MOM.WW.ScadaBridge.CentralUI/Components/Shared/InstanceTreeBuilder.cs

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+using ZB.MOM.WW.ScadaBridge.Commons.Entities.Instances;
+
+namespace ZB.MOM.WW.ScadaBridge.CentralUI.Components.Shared;
+
+/// <summary>
+/// Builds the Instance Picker's area/instance forest from a site's flat area and
+/// instance lists. Pure — no Blazor, no DI, no I/O — so the shape is unit-testable
+/// on its own and the picker component only has to render it.
+/// </summary>
+public static class InstanceTreeBuilder
+{
+    /// <summary>
+    /// Nests the supplied areas by <see cref="Area.ParentAreaId"/> and hangs each area's
+    /// instances beneath it, mirroring the Topology page's ordering: at every level the
+    /// child areas come first (sorted by name, ordinal-ignore-case), then that level's
+    /// instances (sorted by unique name, ordinal-ignore-case). Instances with no area sit
+    /// at the root after the root areas. An area whose parent id points at an area that is
+    /// not in <paramref name="areas"/> is treated as a root, so a stale row can never hide
+    /// a subtree.
+    /// </summary>
+    /// <param name="areas">The site's areas (flat, linked by <see cref="Area.ParentAreaId"/>); null is treated as empty.</param>
+    /// <param name="instances">The site's instances; null is treated as empty.</param>
+    /// <param name="filter">
+    /// Optional case-insensitive substring matched against <see cref="Instance.UniqueName"/>.
+    /// When set, only matching instances are kept along with their ancestor areas; areas left
+    /// with nothing beneath them are dropped. Null or whitespace means no filter.
+    /// </param>
+    /// <returns>The root rows of the forest, never null.</returns>
+    public static IReadOnlyList<InstanceTreeNode> Build(
+        IReadOnlyList<Area>? areas,
+        IReadOnlyList<Instance>? instances,
+        string? filter)
+    {
+        areas ??= [];
+        instances ??= [];
+
+        var needle = filter?.Trim();
+        var hasFilter = !string.IsNullOrEmpty(needle);
+
+        var knownAreaIds = areas.Select(a => a.Id).ToHashSet();
+
+        // Child areas by effective parent id — null for a root or an orphaned area.
+        var areasByParent = areas
+            .OrderBy(a => a.Name, StringComparer.OrdinalIgnoreCase)
+            .ToLookup(a => a.ParentAreaId is int p && knownAreaIds.Contains(p) ? p : (int?)null);
+
+        var instancesByArea = instances
+            .Where(i => !hasFilter || i.UniqueName.Contains(needle!, StringComparison.OrdinalIgnoreCase))
+            .OrderBy(i => i.UniqueName, StringComparer.OrdinalIgnoreCase)
+            .ToLookup(i => i.AreaId);
+
+        return BuildLevel(parentId: null, areasByParent, instancesByArea, hasFilter, ancestors: []);
+    }
+
+    private static List<InstanceTreeNode> BuildLevel(
+        int? parentId,
+        ILookup<int?, Area> areasByParent,
+        ILookup<int?, Instance> instancesByArea,
+        bool hasFilter,
+        HashSet<int> ancestors)
+    {
+        var level = new List<InstanceTreeNode>();
+
+        foreach (var area in areasByParent[parentId])
+        {
+            // Defensive: a cycle in ParentAreaId must never recurse forever.
+            if (!ancestors.Add(area.Id)) continue;
+
+            var node = new InstanceTreeNode($"a:{area.Id}", area.Name, area, Instance: null);
+            node.Children.AddRange(BuildLevel(area.Id, areasByParent, instancesByArea, hasFilter, ancestors));
+            ancestors.Remove(area.Id);
+
+            // With a filter an area survives only if something matched beneath it.
+            if (!hasFilter || node.HasChildren) level.Add(node);
+        }
+
+        level.AddRange(instancesByArea[parentId].Select(i =>
+            new InstanceTreeNode($"i:{i.Id}", i.UniqueName, Area: null, Instance: i)));
+
+        return level;
+    }
+}

src/ZB.MOM.WW.ScadaBridge.CentralUI/Components/Shared/InstanceTreeNode.cs

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+using ZB.MOM.WW.ScadaBridge.Commons.Entities.Instances;
+
+namespace ZB.MOM.WW.ScadaBridge.CentralUI.Components.Shared;
+
+/// <summary>
+/// One row of the Instance Picker tree: an area branch or an instance leaf.
+/// Keys are <c>a:{areaId}</c> for areas and <c>i:{instanceId}</c> for instances.
+/// </summary>
+/// <param name="Key">Stable tree key — <c>a:{areaId}</c> or <c>i:{instanceId}</c>.</param>
+/// <param name="Label">Text rendered for this row.</param>
+/// <param name="Area">The area this node represents, or null for an instance leaf.</param>
+/// <param name="Instance">The instance this node represents, or null for an area branch.</param>
+public sealed record InstanceTreeNode(string Key, string Label, Area? Area, Instance? Instance)
+{
+    /// <summary>Gets the child rows nested under this node (child areas first, then instances).</summary>
+    public List<InstanceTreeNode> Children { get; } = new();
+
+    /// <summary>Gets a value indicating whether this node is a selectable instance leaf.</summary>
+    public bool IsInstance => Instance is not null;
+
+    /// <summary>Gets a value indicating whether this node has any child rows.</summary>
+    public bool HasChildren => Children.Count > 0;
+}

tests/ZB.MOM.WW.ScadaBridge.CentralUI.Tests/Shared/InstanceTreeBuilderTests.cs

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+using ZB.MOM.WW.ScadaBridge.CentralUI.Components.Shared;
+using ZB.MOM.WW.ScadaBridge.Commons.Entities.Instances;
+
+namespace ZB.MOM.WW.ScadaBridge.CentralUI.Tests.Shared;
+
+/// <summary>
+/// Unit tests for <see cref="InstanceTreeBuilder"/> — the pure area/instance forest
+/// behind the Instance Picker combobox (design 2026-09-08).
+/// </summary>
+public class InstanceTreeBuilderTests
+{
+    private static Area MakeArea(int id, string name, int? parentAreaId = null) =>
+        new(name) { Id = id, SiteId = 1, ParentAreaId = parentAreaId };
+
+    private static Instance MakeInstance(int id, string uniqueName, int? areaId = null) =>
+        new(uniqueName) { Id = id, SiteId = 1, AreaId = areaId };
+
+    [Fact]
+    public void Build_NestsAreasByParent_AndPutsRootInstancesAfterRootAreas()
+    {
+        var line1 = MakeArea(1, "Line1");
+        var cellA = MakeArea(2, "Cell A", parentAreaId: 1);
+        var p1 = MakeInstance(10, "P1", areaId: 2);
+        var zulu = MakeInstance(11, "Zulu");
+        var alpha = MakeInstance(12, "Alpha");
+
+        var roots = InstanceTreeBuilder.Build([line1, cellA], [p1, zulu, alpha], filter: null);
+
+        Assert.Equal(new[] { "a:1", "i:12", "i:11" }, roots.Select(n => n.Key));
+
+        var areaNode = roots[0];
+        Assert.Equal("Line1", areaNode.Label);
+        Assert.False(areaNode.IsInstance);
+        Assert.Same(line1, areaNode.Area);
+        Assert.Null(areaNode.Instance);
+        Assert.True(areaNode.HasChildren);
+
+        var cellNode = Assert.Single(areaNode.Children);
+        Assert.Equal("a:2", cellNode.Key);
+        Assert.Equal("Cell A", cellNode.Label);
+        Assert.Same(cellA, cellNode.Area);
+
+        var p1Node = Assert.Single(cellNode.Children);
+        Assert.Equal("i:10", p1Node.Key);
+        Assert.Equal("P1", p1Node.Label);
+        Assert.True(p1Node.IsInstance);
+        Assert.Same(p1, p1Node.Instance);
+        Assert.Null(p1Node.Area);
+        Assert.False(p1Node.HasChildren);
+
+        Assert.Equal("Alpha", roots[1].Label);
+        Assert.Same(alpha, roots[1].Instance);
+        Assert.Equal("Zulu", roots[2].Label);
+        Assert.Same(zulu, roots[2].Instance);
+    }
+
+    [Fact]
+    public void Build_SortsAreasAndInstancesCaseInsensitively()
+    {
+        var beta = MakeArea(1, "beta");
+        var alphaArea = MakeArea(2, "Alpha");
+        var zebra = MakeInstance(10, "zebra");
+        var apple = MakeInstance(11, "Apple");
+
+        var roots = InstanceTreeBuilder.Build([beta, alphaArea], [zebra, apple], filter: null);
+
+        Assert.Equal(new[] { "Alpha", "beta", "Apple", "zebra" }, roots.Select(n => n.Label));
+    }
+
+    [Fact]
+    public void Build_OrphanedArea_BecomesARoot()
+    {
+        // ParentAreaId points at an area that is not in the supplied list.
+        var orphan = MakeArea(5, "Orphan", parentAreaId: 99);
+        var child = MakeInstance(10, "OrphanChild", areaId: 5);
+
+        var roots = InstanceTreeBuilder.Build([orphan], [child], filter: null);
+
+        var root = Assert.Single(roots);
+        Assert.Equal("a:5", root.Key);
+        var leaf = Assert.Single(root.Children);
+        Assert.Equal("i:10", leaf.Key);
+    }
+
+    [Fact]
+    public void Build_Filter_KeepsMatchingInstancesWithAncestors_DropsEmptyBranches()
+    {
+        var line1 = MakeArea(1, "Line1");
+        var cellA = MakeArea(2, "Cell A", parentAreaId: 1);
+        var emptyArea = MakeArea(3, "Line2");
+        var p1 = MakeInstance(10, "P1", areaId: 2);
+        var zulu = MakeInstance(11, "Zulu");
+        var alpha = MakeInstance(12, "Alpha");
+
+        var roots = InstanceTreeBuilder.Build([line1, cellA, emptyArea], [p1, zulu, alpha], filter: "p1");
+
+        var root = Assert.Single(roots);
+        Assert.Equal("a:1", root.Key);
+        var cellNode = Assert.Single(root.Children);
+        Assert.Equal("a:2", cellNode.Key);
+        var leaf = Assert.Single(cellNode.Children);
+        Assert.Equal("i:10", leaf.Key);
+    }
+
+    [Fact]
+    public void Build_Filter_WhitespaceMeansNoFilter()
+    {
+        var line1 = MakeArea(1, "Line1");
+        var p1 = MakeInstance(10, "P1", areaId: 1);
+        var zulu = MakeInstance(11, "Zulu");
+
+        var roots = InstanceTreeBuilder.Build([line1], [p1, zulu], filter: "   ");
+
+        Assert.Equal(new[] { "a:1", "i:11" }, roots.Select(n => n.Key));
+        Assert.Single(roots[0].Children);
+    }
+
+    [Fact]
+    public void Build_NullOrEmptyInputs_ReturnEmpty()
+    {
+        Assert.Empty(InstanceTreeBuilder.Build(null, null, filter: null));
+        Assert.Empty(InstanceTreeBuilder.Build([], [], filter: null));
+        Assert.Empty(InstanceTreeBuilder.Build(null, [], filter: "anything"));
+
+        var orphanInstances = InstanceTreeBuilder.Build(null, [MakeInstance(1, "Solo")], filter: null);
+        Assert.Equal("i:1", Assert.Single(orphanInstances).Key);
+
+        var areasOnly = InstanceTreeBuilder.Build([MakeArea(1, "Line1")], null, filter: null);
+        Assert.Equal("a:1", Assert.Single(areasOnly).Key);
+    }
+
+    [Fact]
+    public void Build_AreaWithNoInstancesAndNoFilter_IsStillShown()
+    {
+        var empty = MakeArea(1, "Empty");
+
+        var roots = InstanceTreeBuilder.Build([empty], [], filter: null);
+
+        var root = Assert.Single(roots);
+        Assert.Equal("a:1", root.Key);
+        Assert.False(root.HasChildren);
+    }
+}