Web client (warp-web) with E2EE, and two sync fixes

apps/web: a Matrix client for the browser on Vue 3, Tailwind and
matrix-js-sdk, built on @warp/ui. Like the admin panel it is an optional,
separate service: warp-web embeds the built app, serves /config.json and
proxies only /_matrix/client and /_matrix/media to the homeserver (or,
with -public-homeserver, lets the browser call it directly).
Sign-in and sign-up with registration tokens, room list, timeline with
back-pagination, text, images, video and files over authenticated media,
local echo with sent/read/failed states, receipts, typing, invites,
creating, joining and leaving rooms, room info, settings, phone layout.
End-to-end encryption through the Rust crypto: encrypted messages and
files, emoji verification, key backup setup and restore.

apps/ui: WRoomItem, WMessageBubble and WComposer from the brand package,
and the icons the client needs.

syncapi fixes found with the client:
- A room joined inside the sync window was sent as the join alone with
  limited: false, so clients thought they had the whole room. It is now
  read like an initial sync; a profile change is not mistaken for a join.
- A live typing notification was reported on every sync, so every long
  poll returned at once while anybody typed. Typing now has a position
  in the sync token and is reported when it changes, including the empty
  list when the last person stops.

Also: Dockerfile, a `web` compose profile, Makefile targets, a CI job
with a proxy smoke test, docs. PLAN.md moves out of the repository.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

README.md

@@ -205,6 +205,10 @@ own process, `warp-admin`, next to the homeserver:
 `docker compose --profile admin up -d`, or see
 [apps/admin](apps/admin/README.md).
 
+The web client is a Matrix client for the browser. It is optional in the
+same way, a process of its own, `warp-web`:
+`docker compose --profile web up -d`, or see [apps/web](apps/web/README.md).
+
 Also in place: argon2id passwords, hashed access and refresh tokens,
 per-endpoint rate limiting, YAML + environment configuration, structured
 logging, graceful shutdown, the storage interfaces with SQLite, PostgreSQL