docs: UI-audit fixes in CLAUDE.md, API, OpenAPI, LANES and READMEs

New params and errors (agents session_ids, sessions awaiting/from/to,
stats tool counts, event labels, cleanup dry_run/INVALID_PURGE_DAYS, lane
start slot auto/ESESSIONLIVE/EUNSUPPORTED), terminal and pane shortcuts,
the shared UI primitives, accent vs accent-solid, lazy routes and the
Settings groups. openapi.yaml regenerated.

server/openapi-extra/override-core.js

@@ -55,7 +55,12 @@ const paths = {
         "ignored rather than rejected. `limit` is clamped to 1–500 (default 50) and " +
         "`offset` is clamped to >= 0 (default 0).\n\n" +
         "Note: each returned event's `data` field is a **JSON-encoded string**, not a " +
-        "nested object — callers must `JSON.parse` it to inspect the payload.",
+        "nested object — callers must `JSON.parse` it to inspect the payload.\n\n" +
+        "Each row also carries its labels, so a list page need not fetch every session " +
+        "and agent to name them: `session_name`, `session_cwd`, `session_lane_id`, " +
+        "`agent_name` and `agent_subagent_type` (nullable; `null` when the session or " +
+        "agent row is missing). They are REST-only — the WebSocket `new_event` frame " +
+        "is unchanged.",
       parameters: [
         {
           in: "query",