feat(worker): per-user box status and lifecycle helpers

Centralize per-user box home-path derivation, status inspection, and
lifecycle (start/stop/restart) in a new box.ts so the HTTP routes and the
terminal WS bridge share one source of truth. Add inspectUserBoxStatus to
docker.ts (single `inspect --format` call, all-null/false on non-zero exit)
and resetBox to user-container.ts (clears the idle timer and drops the
registry entry so a stopped box isn't treated as held).

Manual verification (docker required, after Task 4 wires the routes): with
the worker running and a box up,
`curl -H "Authorization: Bearer $TOKEN" localhost:3921/box/status?user=<you>`
shows running:true + image + startedAt; `POST /box/lifecycle {"action":"stop"}`
flips status to running:false; `start` brings it back.

apps/agent-worker/src/box.ts

@@ -0,0 +1,45 @@
+import path from 'node:path';
+
+import { env } from './env';
+import {
+  ensureUserContainer,
+  inspectUserBoxStatus,
+  stopWorkspaceContainer,
+  userContainerName,
+} from './runtime/docker';
+import { resetBox } from './user-container';
+
+// Per-user box home layout, shared by the HTTP routes and the terminal WS bridge
+// so path derivation lives in exactly one place (must match worker.ts).
+export const boxHomePaths = (username: string) => ({
+  homeDir: path.resolve(env.workdir, 'homes', username),
+  containerHome: path.posix.join('/home', username),
+});
+
+export type BoxStatus = {
+  running: boolean;
+  image: string | null;
+  startedAt: string | null;
+  memoryLimitBytes: number | null;
+  containerName: string;
+};
+
+export const getBoxStatus = async (username: string): Promise<BoxStatus> => {
+  const status = await inspectUserBoxStatus(username);
+  return { ...status, containerName: userContainerName(username) };
+};
+
+export const startBox = async (username: string): Promise<void> => {
+  const { homeDir, containerHome } = boxHomePaths(username);
+  await ensureUserContainer({ username, workdir: homeDir, containerHome });
+};
+
+export const stopBox = async (username: string): Promise<void> => {
+  await stopWorkspaceContainer(userContainerName(username));
+  resetBox(username);
+};
+
+export const restartBox = async (username: string): Promise<void> => {
+  await stopBox(username);
+  await startBox(username);
+};

apps/agent-worker/src/runtime/docker.ts

@@ -214,6 +214,42 @@ export const ensureUserContainer = async (args: {
   return name;
 };
 
+// Inspect the per-user box in one shot. Non-zero exit (no such container) yields
+// an all-null/false status. `--memory 0` means unlimited, which the Go template
+// prints as `0`; we normalize that (and any unparseable value) to null.
+export const inspectUserBoxStatus = async (
+  username: string,
+): Promise<{
+  running: boolean;
+  image: string | null;
+  startedAt: string | null;
+  memoryLimitBytes: number | null;
+}> => {
+  const result = await execa(
+    containerRuntime(),
+    [
+      'inspect',
+      '--format',
+      '{{.State.Running}}|{{.Config.Image}}|{{.State.StartedAt}}|{{.HostConfig.Memory}}',
+      userContainerName(username),
+    ],
+    { reject: false, stdin: 'ignore' },
+  );
+  if (result.exitCode !== 0) {
+    return { running: false, image: null, startedAt: null, memoryLimitBytes: null };
+  }
+  const [runningField, imageField, startedAtField, memoryField] = result.stdout
+    .trim()
+    .split('|');
+  const running = runningField === 'true';
+  return {
+    running,
+    image: imageField || null,
+    startedAt: running ? startedAtField || null : null,
+    memoryLimitBytes: Number(memoryField) || null,
+  };
+};
+
 const shellQuote = (value: string) => `'${value.replaceAll("'", "'\\''")}'`;
 
 // The marker is embedded literally into a `# comment` line and into a `pgrep`

apps/agent-worker/src/user-container.ts

@@ -117,6 +117,15 @@ export const reconcileExistingBoxes = async (): Promise<void> => {
 
 export const runningBoxUsernames = (): Set<string> => new Set(boxes.keys());
 
+// Drop a box from the in-memory registry (used after an explicit stop so a
+// stopped box isn't treated as "held" by the idle reaper or reconcile logic).
+export const resetBox = (username: string): void => {
+  const box = boxes.get(username);
+  if (!box) return;
+  if (box.idleTimer) clearTimeout(box.idleTimer);
+  boxes.delete(username);
+};
+
 export const _resetBoxRegistryForTests = () => {
   for (const box of boxes.values()) {
     if (box.idleTimer) clearTimeout(box.idleTimer);