Chat tabs, chat mode, own modes, compaction notice, CLI binaries again

- Terminals and file managers as tabs of a chat; chat terminals keep running on
  the server (no idle timeout) and re-attach from any device
- "Just chat" in New session and a built-in chat mode with a lean prompt and only
  web tools; custom modes with kind (coding/conversation), read-only and tool picker
- Mode selector as a dropdown
- The chat shows running compactions (automatic: tokens and share of the limit)
  and labels summaries
- Docker image builds and serves the terminal client binaries again
- Fix: atomic session updates; background title/usage writes no longer undo each
  other (auto compaction triggered one turn late)

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

web/src/components/Terminal.tsx

@@ -10,9 +10,10 @@ import { onThemeChange } from "../theme";
 import { toast } from "../dialogs";
 import { Icon } from "./Icon";
 
-interface TermInfo {
+export interface TermInfo {
   id: string;
   cwd: string;
+  session_id?: string | null;
   created_at: number;
   alive: boolean;
   attached: boolean;
@@ -132,7 +133,7 @@ export function TerminalPage({ id, onMenu }: { id?: string; onMenu: () => void }
   );
 }
 
-function TermView({ info }: { info: TermInfo }) {
+export function TermView({ info }: { info: TermInfo }) {
   const t = useT();
   const host = useRef<HTMLDivElement>(null);
   const wsRef = useRef<WebSocket | null>(null);