Add @-mention highlighting, sidebar badge, and push customization (#39)

@username tokens in a sent message are parsed against the room's actual
members (skipping fenced/inline code, so pasted code isn't misread) and
recorded as MessageMention rows, reusing #38's read-tracking and
offline-member broadcast infrastructure rather than building a parallel
notification path:

- Sidebar: a mentioned-and-unread room shows a distinct highlight-
  colored badge instead of (not alongside) the plain unread dot --
  computed the same way as has_unread, just scoped to messages that
  mention the caller, and cleared by the same last_read_at mark-read
  flow.
- Push notifications: a mentioned offline recipient gets "X mentioned
  you: ..." instead of the generic "X: ...", still per-recipient since
  the same message can page some room members and not others.
- Message rendering: a validated @username is highlighted inline,
  implemented by turning it into a `[@username](mention:username)` link
  before markdown parsing and overriding link rendering to style
  `mention:`-scheme links as a span instead of an anchor -- reuses
  markdown-to-jsx's existing parser rather than hand-rolling text-node
  splitting.
- Composer: typing @ opens an autocomplete dropdown of matching room
  members (arrow keys to navigate, Enter/Tab/click to insert, Escape or
  moving the cursor away to dismiss).

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

backend/app/routers/rooms.py

@@ -140,8 +140,9 @@ async def list_my_rooms_endpoint(
             created_at=room.created_at,
             role=role,
             has_unread=has_unread,
+            has_mention=has_mention,
         )
-        for room, role, has_unread in rooms
+        for room, role, has_unread, has_mention in rooms
     ]