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/services/plugin_context.py

@@ -326,6 +326,7 @@ async def _reserve_slot_for_reuse(
         return kept                      # reuse already represented; nothing to do
 
     top_k = cfg["top_k"]
+    _t0 = time.perf_counter()
     reuse = await semantic_search_notes(
         user_id, query,
         limit=1,
@@ -335,6 +336,17 @@ async def _reserve_slot_for_reuse(
         note_type=_REUSE_KINDS,
         scope="browse",
     )
+    # A real semantic query competing for a menu slot — logged like the scored
+    # arm it displaces. Before this, the hit it PUSHED OUT was in
+    # retrieval_logs and the query that pushed it out was not, so the slot
+    # could never be evaluated against what it replaced (#2463; #1038 and
+    # #2085 are gated on this ledger being complete).
+    record_retrieval(
+        user_id=user_id, source="reuse_slot", query=query,
+        threshold=cfg["threshold"], limit=1, project_id=project_id,
+        is_task=None, results=reuse,
+        duration_ms=(time.perf_counter() - _t0) * 1000.0,
+    )
     # Verify the kind rather than trusting the query that asked for it, and
     # dedup on top of exclude_ids. This slot exists FOR reuse kinds — a slot
     # silently spent on something else is worse than no slot, because the line