feat(mtconnect): /sample lag measurement + adaptive count (R06:T-5)

Subscription throughput was hard-capped at SampleCount / SampleIntervalMs with no
lag detection: a machine producing more fell behind the ring buffer forever,
re-baselining every buffer-length with every value backlog-stale.

- The parser carries the header's optional lastSequence; each chunk measures
  lag = lastSequence + 1 - nextSequence and whether it was saturated (full count).
- Three consecutive saturated chunks with a positive (or unknown) lag reopen the
  stream at the cursor reached with count doubled, up to 16x SampleCount (max
  65536), through a new IMTConnectAgentClient.SampleAsync(from, count, ct) overload
  (default implementation ignores count). A raised stream that delivers nothing
  steps back to the last good count; at the ceiling one Warning per pump.
- MTConnectDriver implements IDriverDiagnostics: sampleCount, sampleLag,
  sampleSaturatedChunks, sampleCountRaises on the /hosts bag. The cap is
  documented on SampleCount.

Refs #743

Claude-Session: https://claude.ai/code/session_01Ub9hGmYLQvn9XETzw7CMsT

docs/drivers/MTConnect.md

@@ -73,7 +73,7 @@ below).
 
 ## Capability surface
 
-`MTConnectDriver : IDriver, IReadable, IWritable, ISubscribable, ITagDiscovery, IHostConnectivityProbe, IRediscoverable`
+`MTConnectDriver : IDriver, IReadable, IWritable, ISubscribable, ITagDiscovery, IHostConnectivityProbe, IRediscoverable, IDriverDiagnostics`
 (`src/Drivers/ZB.MOM.WW.OtOpcUa.Driver.MTConnect/MTConnectDriver.cs`).
 
 `IWritable` landed 2026-08-05 (`b29623cf`), against the Agent's `AllowPut`
@@ -92,6 +92,7 @@ request/response handshake — is a different mechanism and remains deferred; se
 | `ISubscribable` | `SubscribeAsync`/`OnDataChange` — the shared `/sample` long-poll pump | **The production data path** |
 | `IHostConnectivityProbe` | periodic `/probe` under `Probe.*` | No consumer wires it today — see [Known limitations](#known-limitations) |
 | `IRediscoverable` | watches the Agent's `Header.instanceId` | No consumer wires it today — see [Known limitations](#known-limitations) |
+| `IDriverDiagnostics` | `GetDiagnostics()` — `/sample` effective count, lag, saturated chunks, count raises | Shown on `/hosts` (review 2026-10-21 T-5) |
 | `IAlarmSource` | CONDITION observations off the same `/sample` pump → Part 9 transitions keyed by the alarm tag's RawPath | Opt-in per raw tag (`alarm` object) — see [CONDITION alarms](#condition-alarms-626) |
 
 ### Feature status at a glance (#613)
@@ -159,7 +160,7 @@ Read off `MTConnectDriverOptions` / `MTConnectDriverConfigDto`
 | `DeviceName` | `null` | **Double duty.** (1) Scopes requests to `{AgentUri}/{DeviceName}/...`; `null` = whole Agent. (2) The write path's fallback device — the device a write is addressed to when the probe model does not say which device declared the DataItem (see [Write-back](#write-back--observation-injection-off-by-default)) |
 | `RequestTimeoutMs` | `5000` | Per-call deadline for `/probe` and `/current` |
 | `SampleIntervalMs` | `1000` | The Agent's `/sample?interval=` query param |
-| `SampleCount` | `1000` | The Agent's `/sample?count=` query param |
+| `SampleCount` | `1000` | The Agent's `/sample?count=` query param. **Caps subscription throughput** at `SampleCount / SampleIntervalMs` — see [Subscribe](#subscribe--the-sample-pump) for the adaptive raise |
 | `HeartbeatMs` | `10000` | The Agent's `/sample?heartbeat=` query param — also the watchdog's liveness window |
 | `Probe.Enabled` / `Probe.IntervalMs` / `Probe.TimeoutMs` | `true` / `5000` / `2000` | Background connectivity-probe knobs (mirrors `ModbusProbeOptions`) |
 | `Reconnect.MinBackoffMs` / `MaxBackoffMs` / `BackoffMultiplier` | `0` / `30000` / `2.0` | Geometric backoff after a failed request or a dropped `/sample` stream |
@@ -333,6 +334,17 @@ the two need disambiguating, not just OR-ing together). On a changed
 `/hosts` page — see [Known limitations](#known-limitations) for what that does
 and does not do.
 
+**Lag measurement and the adaptive `count` (review 2026-10-21 T-5).** Throughput is capped at `SampleCount`
+observations per chunk, one chunk per `SampleIntervalMs`; a machine producing more used to fall behind the ring
+buffer forever, re-baselining every buffer-length (dropping intermediate transitions) with nothing surfacing it.
+Each chunk is now measured: `lag = lastSequence + 1 − nextSequence` (unknown when the Agent omits `lastSequence`)
+and whether it was **saturated** (carried the full `count`). Three consecutive saturated chunks with a positive (or
+unknown) lag reopen the stream at the cursor reached with `count` doubled, up to 16× `SampleCount` (max 65 536). A
+raised stream that delivers nothing (an Agent refusing the larger count) steps back to the last count that delivered
+and stops raising; at the ceiling a still-behind stream logs one Warning per pump. Every new pump starts from the
+configured `SampleCount`. The driver now implements `IDriverDiagnostics`: `sampleCount` (effective), `sampleLag`,
+`sampleSaturatedChunks` and `sampleCountRaises` ride the `/hosts` diagnostics bag.
+
 **A pump carries the session generation it was started against (review 2026-10-21 T-1).** A lifecycle restart
 retires the running pump (or abandons it after its bounded teardown wait); if that pump finishes after the new
 session is installed, its cursor publish, a late chunk and a late re-baseline are all dropped — checked under the