feat(tasks): SessionStart reads the claim — a compaction gets its work back (milestone 381 step 3)

The claim now pays rent to the session that set it. The SessionStart hook
sends the host's `source` and the session id; the server renders a claim
section by source (task_claims.render_claims):

- compact / clear: the work this session had claimed, each with its two
  latest log entries, so a compacted session resumes from the record
  rather than from a count of open tasks.
- startup / clear: other sessions' live claims (may still be running) and
  in-progress tasks whose claim went quiet (abandoned mid-task).
- fork: the same, framed as "two sessions may now hold this".
- resume, or no source sent: nothing.

The task sidebar shows a live claim as "Being worked" and a dead one on
open work as "Went quiet", so the operator sees a session die mid-task.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/scribe/routes/plugin.py

@@ -70,10 +70,16 @@ async def session_context():
             send it when a `.scribe` marker file names a project. Takes
             precedence over `repo`. Access-checked like any other read — an id
             this account cannot read loads no project rather than failing.
+        source (optional str) — the host's SessionStart source (startup,
+            resume, compact, clear, fork); decides what the claim section says.
+        session_id (optional str) — the session's id, so a claim bound to it
+            reads as this session's own (milestone 381).
     """
     project_id, _repo, unbound_repo = await _project_scope()
     result = await plugin_ctx_svc.build_session_context(
-        g.user.id, project_id, unbound_repo=unbound_repo
+        g.user.id, project_id, unbound_repo=unbound_repo,
+        source=(request.args.get("source") or "").strip()[:20],
+        session_id=(request.args.get("session_id") or "").strip()[:200],
     )
     return jsonify(result)