feat(coach): full-history search + pagination; document the labs watchdog

Coach conversation history was capped at the rail's first ~20 threads and
searched only that loaded page. The rail and the standalone conversations
page now walk the caller's entire history via cursor pagination
(useInfiniteQuery + a scroll sentinel), and search runs server-side against
the conversation title (GET /api/insights/chat?q=) instead of filtering an
already-truncated client array.

Also extends the "automatic screening" info line in the metric catalog to
name the labs "what changed since your last panel" card alongside the
rhythm/breathing/health-status watchdogs it already covered — it un-mounts
the same way when there's nothing to flag and was missing from the copy.

docs/api/openapi.yaml

@@ -5068,8 +5068,10 @@ paths:
       description: v1.18.0 — cursor-paginated list of the caller's Coach conversations for the history rail, most-recent
         activity first. Metadata only (id, title, timestamps, message count); message bodies are not decrypted here.
         `limit` defaults to 20, capped at 50; pass the returned `nextCursor` back as `cursor` for the next page (null at
-        the end). Coach-gated (`requireAssistantSurface("coach")`); a disabled surface 403s. Auth via cookie or Bearer;
-        the owner is narrowed from the session.
+        the end). v1.30.2 — optional `q` narrows the page to conversations whose TITLE contains the text
+        (case-insensitive substring, capped at 200 chars); message bodies are encrypted at rest and are not searched.
+        Coach-gated (`requireAssistantSurface("coach")`); a disabled surface 403s. Auth via cookie or Bearer; the owner
+        is narrowed from the session.
       parameters:
         - name: cursor
           in: query
@@ -5086,6 +5088,14 @@ paths:
             maximum: 50
             default: 20
           description: Page size. Defaults to 20, capped at 50.
+        - name: q
+          in: query
+          required: false
+          schema:
+            type: string
+            maxLength: 200
+          description: v1.30.2 — case-insensitive substring filter over the conversation TITLE only (message bodies are encrypted
+            and not searched). Omit for the unfiltered list.
       responses:
         "200":
           description: A page of the caller's conversations.