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/BoothScreen.tsx

@@ -207,7 +207,8 @@ export function BoothScreen() {
 
   // Apply the live-feed filters. Source maps to booth (operator-initiated `manual`)
   // vs reader (device-initiated: wiegand/lpr/qr/ticket). Search spans identity,
-  // subscriber label, and any advisory plate on the payload.
+  // subscriber label, and the enriched advisory plate (`e.plate` — the displayed field;
+  // the plate is NOT in the signed payload, so `payload.plate` would never match).
   const fq = feedSearch.trim().toLowerCase();
   const events = scoped.filter((e) => {
     if (feedType && feedCat(e.type) !== feedType) return false;
@@ -217,7 +218,7 @@ export function BoothScreen() {
       if (feedSrc === "booth" ? !isBooth : isBooth) return false;
     }
     if (fq) {
-      const hay = `${e.identity ?? ""} ${e.subscriberLabel ?? ""} ${e.payload?.plate ?? ""}`.toLowerCase();
+      const hay = `${e.identity ?? ""} ${e.subscriberLabel ?? ""} ${e.plate ?? ""}`.toLowerCase();
       if (!hay.includes(fq)) return false;
     }
     return true;