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>

apps/web/package.json

@@ -0,0 +1,29 @@
+{
+  "name": "@warp/web",
+  "version": "0.0.0",
+  "private": true,
+  "description": "Warp web client: a Matrix client for the browser",
+  "type": "module",
+  "scripts": {
+    "dev": "vite",
+    "build": "vue-tsc --noEmit && vite build",
+    "preview": "vite preview",
+    "typecheck": "vue-tsc --noEmit"
+  },
+  "dependencies": {
+    "@warp/ui": "workspace:*",
+    "matrix-js-sdk": "^44.0.0",
+    "pinia": "^3.0.3",
+    "vue": "^3.5.22",
+    "vue-router": "^4.5.1"
+  },
+  "devDependencies": {
+    "@tailwindcss/vite": "^4.1.14",
+    "@types/node": "^22.18.10",
+    "@vitejs/plugin-vue": "^6.0.1",
+    "tailwindcss": "^4.1.14",
+    "typescript": "~5.9.3",
+    "vite": "^7.1.9",
+    "vue-tsc": "^3.1.1"
+  }
+}