feat(web): a play-now button that skips the room code

QuickMatch/CancelQuickMatch join and leave the pairing queue; the
store tracks the wait as `queued` and clears it the moment a RoomState
seats the connection. The /online screen shows a waiting panel with
elapsed time, a cancel button, and — past 20 seconds — a nudge toward
the bot; leaving the page while queued cancels it. Adds the two new
error codes and a sentence to the room-code rules copy.

web/tests/game-store.test.js

@@ -533,6 +533,28 @@ describe('pong', () => {
 	});
 });
 
+describe('quickMatchStatus', () => {
+	it('flags the wait while queued', () => {
+		const store = createGameStore();
+		store.apply(msg('quickMatchStatus', { queued: true }));
+		expect(store.state.queued).toBe(true);
+	});
+
+	it('ends the wait once the queue answers false', () => {
+		const store = createGameStore();
+		store.apply(msg('quickMatchStatus', { queued: true }));
+		store.apply(msg('quickMatchStatus', { queued: false }));
+		expect(store.state.queued).toBe(false);
+	});
+
+	it('ends the wait the moment a room seats this connection, even with no prior status', () => {
+		const store = createGameStore();
+		store.apply(msg('quickMatchStatus', { queued: true }));
+		store.apply(pair());
+		expect(store.state.queued).toBe(false);
+	});
+});
+
 describe('chat', () => {
 	/** @param {object} fields */
 	function line(fields) {

web/tests/ws-client.test.js

@@ -7,7 +7,7 @@
 
 import { beforeEach, describe, expect, it } from 'vitest';
 import { create, toBinary } from '@bufbuild/protobuf';
-import { PROTOCOL_VERSION } from '../src/lib/ws/messages.js';
+import { PROTOCOL_VERSION, cancelQuickMatch, quickMatch } from '../src/lib/ws/messages.js';
 import {
 	ClientMessageSchema,
 	ServerMessageSchema
@@ -351,6 +351,28 @@ describe('frames', () => {
 	});
 });
 
+describe('quick match', () => {
+	it('encodes a QuickMatch frame the transport will carry as-is', async () => {
+		const h = setup();
+		h.client.connect();
+		h.last().open();
+		h.client.send(quickMatch());
+
+		const sent = await sentMessages(h.last());
+		expect(sent.at(-1).payload.case).toBe('quickMatch');
+	});
+
+	it('encodes a CancelQuickMatch frame the transport will carry as-is', async () => {
+		const h = setup();
+		h.client.connect();
+		h.last().open();
+		h.client.send(cancelQuickMatch());
+
+		const sent = await sentMessages(h.last());
+		expect(sent.at(-1).payload.case).toBe('cancelQuickMatch');
+	});
+});
+
 describe('handshake ordering', () => {
 	it('sends Hello before announcing the connection is open', async () => {
 		// The server refuses everything until the handshake lands, so a listener