Fix desktop tray unread indicator: clear only on genuine room entry

The tray indicator must stay visible while a message is unread and
clear only when the user actually opens the room containing it --
never merely because the window was shown, focused, restored, or
opened from the tray.

Adds window.dsDesktop.roomOpened() (called exactly once per genuine
transition to a real room id, via useDesktopRoomBridge) and wires up
window.dsDesktop.setUnreadCount() (declared but never actually called
before this) to fire whenever the unread-room count changes. Both are
no-ops in browser builds, matching this bridge's existing optional-
chaining convention.

Frontend unread state stays authoritative -- clearRoomIndicators is
pulled out of ChatShellPage as a pure function (same behavior, now
directly testable) so opening one room only clears that room's
unread/mention flags, leaving every other room's state untouched.

Also adds a frontend test runner (vitest + React Testing Library) --
none existed in this project before. 10 new tests cover: roomOpened
firing once on entry, not refiring on an unrelated rerender with the
same room id, refiring on a genuine room-to-room transition, never
firing with no room id, setUnreadCount firing independently of
roomOpened, clearing one room preserving every other room's unread
state, and the desktop bridge remaining fully optional.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

frontend/src/lib/roomIndicators.test.ts

@@ -0,0 +1,56 @@
+import { describe, expect, it } from 'vitest'
+import type { MyRoomItem } from '../types'
+import { clearRoomIndicators } from './roomIndicators'
+
+function makeRoom(overrides: Partial<MyRoomItem> & { id: string }): MyRoomItem {
+  return {
+    name: overrides.id,
+    description: null,
+    is_private: false,
+    is_dm: false,
+    is_archived: false,
+    owner_id: 'owner',
+    created_at: '2026-01-01T00:00:00Z',
+    role: 'member',
+    has_unread: false,
+    has_mention: false,
+    dm_partner: null,
+    email_notifications: false,
+    ...overrides,
+  }
+}
+
+describe('clearRoomIndicators', () => {
+  it('clears has_unread and has_mention on the matching room', () => {
+    const rooms = [makeRoom({ id: 'room-1', has_unread: true, has_mention: true })]
+    const result = clearRoomIndicators(rooms, 'room-1')
+    expect(result[0].has_unread).toBe(false)
+    expect(result[0].has_mention).toBe(false)
+  })
+
+  it('preserves unread state on every other room', () => {
+    const rooms = [
+      makeRoom({ id: 'room-1', has_unread: true, has_mention: true }),
+      makeRoom({ id: 'room-2', has_unread: true, has_mention: false }),
+      makeRoom({ id: 'room-3', has_unread: false, has_mention: false }),
+    ]
+    const result = clearRoomIndicators(rooms, 'room-1')
+    const room2 = result.find((r) => r.id === 'room-2')
+    const room3 = result.find((r) => r.id === 'room-3')
+    expect(room2?.has_unread).toBe(true)
+    expect(room3?.has_unread).toBe(false)
+  })
+
+  it('leaves untouched rooms as the same object reference', () => {
+    const room2 = makeRoom({ id: 'room-2', has_unread: true })
+    const rooms = [makeRoom({ id: 'room-1', has_unread: true }), room2]
+    const result = clearRoomIndicators(rooms, 'room-1')
+    expect(result[1]).toBe(room2)
+  })
+
+  it('is a no-op if the room id is not found', () => {
+    const rooms = [makeRoom({ id: 'room-1', has_unread: true })]
+    const result = clearRoomIndicators(rooms, 'does-not-exist')
+    expect(result[0].has_unread).toBe(true)
+  })
+})