feat: cross-chat search UX (top-bar + results page) (T100)

Wires T93's `search_all_memories` service into a small read-only HTML
surface so users can find a memory across every chat in the database.

* `chat/web/search.py` (new): GET `/search?q=...` runs the FTS service
  with k=50, hydrates each row with bot name + scene timestamp, and
  renders `search.html`. Empty `q` short-circuits to no results so the
  top-bar form can submit even with an empty input.
* `chat/templates/search.html` (new): empty-state placeholder, results
  list with chat-level "Open chat" links (`/chats/{chat_id}` — memories
  don't carry an event_id today, so no per-turn anchor).
* `chat/templates/layout.html`: append a small `<form>` to the rail
  nav, additive only.
* `chat/app.py`: register `search_router` (additive import + include).
* `tests/test_search_ux.py`: 3 tests — multi-chat results, empty-query
  placeholder, chat link.

tests/test_search_ux.py

@@ -0,0 +1,135 @@
+"""T100 (Phase 4): cross-chat search UX (top-bar + results page).
+
+Verifies the FastAPI ``/search`` route that wraps T93's
+``search_all_memories`` service:
+
+* ``/search?q=...`` returns 200 + an HTML page that lists matches drawn
+  from MULTIPLE chats (not just the current one) and links each result
+  back to ``/chats/{chat_id}``.
+* ``/search`` with no query renders the page in its empty state with a
+  "enter a query" placeholder and no result rows (avoids hitting the
+  FTS index with an invalid empty MATCH).
+* Result links navigate to the originating chat so users can pick up
+  the thread where the memory came from.
+"""
+
+from __future__ import annotations
+
+from pathlib import Path
+
+import pytest
+from fastapi.testclient import TestClient
+
+from chat.app import app
+from chat.db.connection import open_db
+from chat.eventlog.log import append_event
+from chat.eventlog.projector import project
+import chat.state.memory  # noqa: F401  (registers memory_written handler)
+
+
+@pytest.fixture
+def client(tmp_path, monkeypatch):
+    config_path = tmp_path / "config.toml"
+    config_path.write_text('featherless_api_key = "test"\n')
+    monkeypatch.setenv("CHAT_CONFIG_PATH", str(config_path))
+    monkeypatch.setenv("CHAT_DB_PATH", str(tmp_path / "test.db"))
+    with TestClient(app) as c:
+        yield c
+
+
+def _seed_two_chats_with_memories(db_path: Path) -> None:
+    """Seed: a ``you_entity``, two bots, two chats, and one ``rabbit``
+    memory per chat. Two-chat seeding lets the cross-chat assertion
+    actually distinguish "both chats appear" from "only the current
+    one does"."""
+    with open_db(db_path) as conn:
+        append_event(
+            conn,
+            kind="you_authored",
+            payload={"name": "Me", "pronouns": "", "persona": ""},
+        )
+        for bot_id, chat_id in (("bot_a", "chat_a"), ("bot_b", "chat_b")):
+            append_event(
+                conn,
+                kind="bot_authored",
+                payload={
+                    "id": bot_id,
+                    "name": bot_id.upper(),
+                    "persona": "thoughtful",
+                    "voice_samples": [],
+                    "traits": [],
+                    "backstory": "",
+                    "initial_relationship_to_you": "friend",
+                    "kickoff_prose": "kickoff",
+                },
+            )
+            append_event(
+                conn,
+                kind="chat_created",
+                payload={
+                    "id": chat_id,
+                    "host_bot_id": bot_id,
+                    "initial_time": "2026-04-26T20:00:00+00:00",
+                    "narrative_anchor": "Day 1",
+                    "weather": "",
+                },
+            )
+            append_event(
+                conn,
+                kind="memory_written",
+                payload={
+                    "owner_id": bot_id,
+                    "chat_id": chat_id,
+                    "pov_summary": f"the rabbit darted across {chat_id}",
+                    "witness_you": 1,
+                    "witness_host": 1,
+                    "witness_guest": 0,
+                    "source": "direct",
+                    "reliability": 1.0,
+                    "significance": 1,
+                    "pinned": 0,
+                    "auto_pinned": 0,
+                },
+            )
+        project(conn)
+
+
+def test_search_returns_results_from_multiple_chats(client, tmp_path):
+    """A single ``/search?q=rabbit`` must surface matches from BOTH
+    chats — the whole point of the cross-chat search box is that it
+    isn't owner-scoped."""
+    _seed_two_chats_with_memories(tmp_path / "test.db")
+    resp = client.get("/search?q=rabbit")
+    assert resp.status_code == 200
+    body = resp.text
+    # Both chats' memory snippets must appear in the rendered page.
+    assert "chat_a" in body
+    assert "chat_b" in body
+    assert "rabbit" in body.lower()
+
+
+def test_empty_query_renders_placeholder_not_results(client, tmp_path):
+    """``/search`` with no query renders the page in its empty state.
+
+    The placeholder copy is a contract with the user — they should see
+    "enter a query" rather than an empty result list that looks like a
+    no-match. Also: the FTS short-circuit means there are no result
+    rows to leak into the body."""
+    _seed_two_chats_with_memories(tmp_path / "test.db")
+    resp = client.get("/search")
+    assert resp.status_code == 200
+    body = resp.text.lower()
+    assert "enter a query" in body
+    # Seeded "rabbit" memories must NOT appear: empty query => no results.
+    assert "the rabbit darted" not in resp.text
+
+
+def test_result_links_navigate_to_chat(client, tmp_path):
+    """Each result links back to its originating chat so the user can
+    reopen the thread where the memory was first witnessed."""
+    _seed_two_chats_with_memories(tmp_path / "test.db")
+    resp = client.get("/search?q=rabbit")
+    assert resp.status_code == 200
+    # The link target is chat-level (memories don't carry an event_id
+    # column today, so we don't deep-link to a specific turn).
+    assert 'href="/chats/chat_a"' in resp.text