fix(booth): backfill the live-feed plate + make plate search work

Two booth feed fixes:

- Plate not showing until refresh. Plate recognition is async/advisory
  (snapshot.ts recognizePlate → a kind:"read" device_event keyed by the session
  identity), so it lands AFTER the entry/exit event already shipped over the WS
  without a plate; a refresh re-fetched via the bulk enrich path and showed it.
  Added a `plate-recognized` bus event (device-events.ts) emitted when the read
  is written; ws.ts forwards it; the client patchPlate(identity, plate)
  (live-store) backfills the already-rendered feed row in place and invalidates
  the Query-owned active-sessions list. No refresh.

- Plate search didn't filter. Both the live-feed (BoothScreen) and active-sessions
  (ActiveSessions) search haystacks matched the wrong field — the displayed plate
  is the ENRICHED top-level e.plate/s.plate (set by enrichEvent), not payload.plate
  (the plate is unsigned, never in the signed payload). Switched the haystacks to
  the displayed field.

Claude-Session: https://claude.ai/code/session_01Xcm6ikLgGoCxxHrxtjkk5V

apps/web/src/ActiveSessions.tsx

@@ -83,7 +83,8 @@ export function ActiveSessions({ onPick }: { onPick: (identity: string) => void
       if (kind === "subscription" && !s.subscription) return false;
       if (status && statusOf(s) !== status) return false;
       if (q) {
-        const hay = `${s.identity} ${s.subscriptionHolder ?? ""}`.toLowerCase();
+        // Include the enriched plate (`s.plate`, the displayed badge) so a plate search hits.
+        const hay = `${s.identity} ${s.subscriptionHolder ?? ""} ${s.plate ?? ""}`.toLowerCase();
         if (!hay.includes(q)) return false;
       }
       return true;