feat(booth): blink the Entry/Exit lights on radar presence (mirror relay 3)

The on-screen Hyrje/Dalje barrier lights were 2-state (green=free / red=busy)
off the camera lane-status only — they couldn't show the radar-only "detected,
not yet confirmed" state that makes the physical button lamp (relay 3) blink.
Now they mirror the lamp's 3-state rule per lane:
  radar present + camera not busy → BLINK green↔red (~1 Hz)
  camera busy                     → SOLID red
  otherwise                       → SOLID green

End-to-end:
- LanePresence (lane-presence.ts): subscribes to deviceEvents.onInput, resolves
  each presence edge to its lane via the new direction-agnostic presenceLaneOf()
  (device-resolve.ts) — entry AND exit, unlike the entry-gated relayForPresence
  the one-car-one-ticket gate uses — and emits a lane-presence {entry,exit} bus
  event on change. Wired in server.ts (start + onClose).
- WS forwards it (hello snapshot + push) into live-store.radar.
- BarrierLight (BoothScreen.tsx) is now 3-state; blinks via the .lane-blink
  keyframe (index.css), which holds solid-red under prefers-reduced-motion.

Same input + same rule as the lamp, so the screen and the post never disagree.

A new test (lane-presence.test.ts) caught a real bug: the first cut reused
relayForPresence, so the EXIT lane never resolved (it's entry-gated) and never
blinked — presenceLaneOf fixes it. Covers entry/exit independence, de-dupe
across several radars on one lane, and ignoring non-presence inputs.

Full workspace build/lint/test green (185 server tests). Updated the
button-light-indicator wiki page ("On-screen twin").

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

apps/server/src/routes/ws.ts

@@ -2,10 +2,11 @@ import type { FastifyInstance } from "fastify";
 import type { Db } from "@parking/db";
 import type { LedgerEvent } from "@parking/shared";
 import { roleHasPermissions } from "../auth.js";
-import { deviceEvents, type LaneStatusEvent } from "../device-events.js";
+import { deviceEvents, type LaneStatusEvent, type LanePresenceEvent } from "../device-events.js";
 import { enrichEvent } from "../event-enrich.js";
 import type { DeviceMonitor } from "../device-monitor.js";
 import type { LaneStatus } from "../lane-status.js";
+import type { LanePresence } from "../lane-presence.js";
 import { getOccupancy } from "../occupancy.js";
 
 // Live booth feed over a WebSocket. The booth UI opens ONE socket and receives
@@ -53,17 +54,25 @@ function isAllowedOrigin(origin: string | undefined, host: string | undefined):
 }
 
 type OutMsg =
-  | { kind: "hello"; occupancy: ReturnType<typeof getOccupancy>; devices: unknown; lanes: LaneStatusEvent }
+  | {
+      kind: "hello";
+      occupancy: ReturnType<typeof getOccupancy>;
+      devices: unknown;
+      lanes: LaneStatusEvent;
+      radar: LanePresenceEvent;
+    }
   | { kind: "ledger"; event: unknown; occupancy: ReturnType<typeof getOccupancy> }
   | { kind: "printer-status"; event: unknown }
   | { kind: "device-status"; event: unknown }
-  | { kind: "lane-status"; lanes: LaneStatusEvent };
+  | { kind: "lane-status"; lanes: LaneStatusEvent }
+  | { kind: "lane-presence"; radar: LanePresenceEvent };
 
 export async function wsRoutes(
   app: FastifyInstance,
   db: Db,
   deviceMonitor: DeviceMonitor,
   laneStatus: LaneStatus,
+  lanePresence: LanePresence,
 ): Promise<void> {
   app.get(
     "/api/ws",
@@ -96,7 +105,13 @@ export async function wsRoutes(
 
       // Initial snapshot so the client renders immediately, before any event:
       // occupancy AND the current device-status set (for the footer).
-      send({ kind: "hello", occupancy: getOccupancy(db), devices: deviceMonitor.snapshot(), lanes: laneStatus.snapshot() });
+      send({
+        kind: "hello",
+        occupancy: getOccupancy(db),
+        devices: deviceMonitor.snapshot(),
+        lanes: laneStatus.snapshot(),
+        radar: lanePresence.snapshot(),
+      });
 
       // Subscribe to the live buses. Each handler recomputes occupancy from the
       // ledger (cheap fold) so the pushed count is always authoritative.
@@ -117,12 +132,17 @@ export async function wsRoutes(
       const offLane = deviceEvents.onLaneStatus((lanes) => {
         send({ kind: "lane-status", lanes });
       });
+      // Lane RADAR presence (presence-input edge → barrier-light blink). Advisory.
+      const offPresence = deviceEvents.onLanePresence((radar) => {
+        send({ kind: "lane-presence", radar });
+      });
 
       socket.on("close", () => {
         offLedger();
         offPrinter();
         offDevice();
         offLane();
+        offPresence();
       });
     },
   );