feat(notifications): honor chat mute in web realtime alerts

docs/api-reference.md

@@ -231,6 +231,7 @@ All fields are optional.
   "is_saved": false,
   "archived": false,
   "pinned": false,
+  "muted": false,
   "unread_count": 3,
   "unread_mentions_count": 1,
   "pinned_message_id": null,

docs/core-checklist-status.md

@@ -34,7 +34,7 @@ Legend:
 25. Admin Rights - `PARTIAL` (delete/pin/edit info + explicit ban API for groups/channels; integration tests cover channel member read-only, channel admin full-delete, channel message delete-for-all permissions, group profile edit permissions, and owner-only role management rules; remaining UX moderation tools limited)
 26. Channels - `PARTIAL` (create/post/edit/delete/subscribe/unsubscribe; UX edge-cases still polishing)
 27. Channel Types - `DONE` (public/private)
-28. Notifications - `PARTIAL` (browser notifications + mute/settings; no mobile push infra)
+28. Notifications - `PARTIAL` (browser notifications + mute/settings; chat mute is now propagated in chat list payload and honored by web realtime notifications with mention override; no mobile push infra)
 29. Archive - `DONE`
 30. Blacklist - `DONE`
 31. Privacy - `PARTIAL` (avatar/last-seen/group-invites + PM policy `everyone|contacts|nobody`; group-invite `nobody` is available in API and web settings; integration tests cover PM policy matrix (`everyone/contacts/nobody`), group-invite policy matrix (`everyone/contacts/nobody`), and private chat counterpart visibility for `nobody/contacts`, remaining UX/matrix hardening)