fix(telemetry): the two invisible retrievals log, and /api/search takes scope

#2463, the remaining findings (finding 3 landed with f11a547).

## The reuse slot logs (source: reuse_slot)

A real semantic query competing for an auto-inject menu slot, and the ledger
was asymmetric: the scored hit it DISPLACED was in retrieval_logs, the query
that displaced it was not — so the slot could never be evaluated against what
it replaced. #1038 and #2085 are gated on this ledger being complete.

## Browse search logs (source: browse_search)

The human's main search surface, and it logged nothing — so retrieval_logs
claimed the web's search was /api/search. Measured while fixing: /api/search
has ZERO frontend consumers; the web UI searches through /api/knowledge
exclusively. The table wasn't just under-describing the UI, it was describing
a surface the UI never touches.

The task's check — does folding human queries into the corpus skew the
precision signal thresholds are tuned against? — is answered by the source
column: distinct values (browse_search, reuse_slot beside the existing four)
mean tuning includes or excludes human traffic deliberately rather than by
accident. Same resolution as the mcp_/rest_ split in note_usage_events.

## /api/search takes project_id (and logs it)

The route logged project_id=None unconditionally while the MCP tool insists
the agent pass the active project. Now optional, default global: with no
frontend consumer, this route serves API callers, and an API caller states
its scope explicitly — the default-scope UI decision the task flagged is moot
until a UI actually consumes the route, which is recorded rather than guessed.

Refs #2463

src/scribe/routes/search.py

@@ -36,22 +36,24 @@ async def search_route():
     content_type = request.args.get("content_type", "all")
     limit = min(request.args.get("limit", 10, type=int), 50)
     is_task = _content_type_to_is_task(content_type)
-    # Same association filter the MCP tool takes (#33). The project filter this
-    # route is still missing is #2463's — it carries a default-scope UI decision
-    # this change must not preempt.
+    # Same association filters the MCP tool takes (#33). Optional, default
+    # global: this route has NO frontend consumer today (measured 2026-08-08 —
+    # the web UI searches through /api/knowledge), so it serves API callers,
+    # and an API caller states its scope explicitly.
     system_id = request.args.get("system_id", type=int)
+    project_id = request.args.get("project_id", type=int)
 
     t0 = time.perf_counter()
     results = await semantic_search_notes(
         uid, q, limit=limit, is_task=is_task, threshold=_REST_SEARCH_THRESHOLD,
-        system_id=system_id,
+        project_id=project_id, system_id=system_id,
         # The user typed this, so it reaches everything they may read.
         scope="read",
     )
     record_retrieval(
         user_id=uid, source="rest_search", query=q,
         threshold=_REST_SEARCH_THRESHOLD, limit=limit,
-        project_id=None, is_task=is_task, results=results,
+        project_id=project_id, is_task=is_task, results=results,
         duration_ms=(time.perf_counter() - t0) * 1000.0,
     )
     owners = await owner_names_for(