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/src/components/StartChatDialog.vue

@@ -0,0 +1,67 @@
+<script setup lang="ts">
+import { ref, watch } from 'vue'
+import { WBanner, WButton, WDialog, WTextField } from '@warp/ui'
+import { errorMessage, isUserId, toUserId } from '@/lib/format'
+import { useChat } from '@/stores/chat'
+import { useSession } from '@/stores/session'
+
+const open = defineModel<boolean>('open', { default: false })
+const emit = defineEmits<{ started: [roomId: string] }>()
+
+const chat = useChat()
+const session = useSession()
+const who = ref('')
+const busy = ref(false)
+const error = ref('')
+
+watch(open, (v) => {
+  if (v) {
+    who.value = ''
+    error.value = ''
+  }
+})
+
+async function submit() {
+  const userId = toUserId(who.value, session.serverName)
+  if (!isUserId(userId)) return
+  if (userId === session.userId) {
+    error.value = 'That’s your own Matrix ID.'
+    return
+  }
+  busy.value = true
+  error.value = ''
+  try {
+    const roomId = await chat.startDirect(userId)
+    open.value = false
+    emit('started', roomId)
+  } catch (e) {
+    error.value = errorMessage(e)
+  } finally {
+    busy.value = false
+  }
+}
+</script>
+
+<template>
+  <WDialog v-model:open="open" title="Start chat" :persistent="busy">
+    <form id="start-chat" class="flex flex-col gap-4" @submit.prevent="submit">
+      <WTextField
+        v-model="who"
+        wide
+        mono
+        label="Who"
+        :hint="`A username on ${session.serverName}, or a full Matrix ID like @maja:warp.example`"
+        autocomplete="off"
+        autocapitalize="off"
+        spellcheck="false"
+        required
+        autofocus
+      />
+      <WBanner v-if="error" tone="danger">{{ error }}</WBanner>
+    </form>
+    <template #actions>
+      <WButton variant="ghost" :disabled="busy" @click="open = false">Cancel</WButton>
+      <WButton type="submit" form="start-chat" variant="primary" :loading="busy" :disabled="!who.trim()">Start chat</WButton>
+    </template>
+  </WDialog>
+</template>