feat(worker): /box status, lifecycle, tree, and file HTTP routes

Wire the box helpers into the worker HTTP server as /box/* routes,
authed by the internal bearer token like every other worker route.
Adds a boxRoute matcher (/^\/box\/(status|lifecycle|tree|file)$/) and
dispatches before jobRoute; missing user -> 400, unknown lifecycle
action -> 400, containment throws -> 400 (server keeps serving).

Manual verification (harness on :3922, internal token, user gabriel):
  GET  /box/status?user=gabriel        -> 200 {"status":{...running:false...}}
  GET  /box/status  (no user)          -> 400 {"error":"Missing user"}
  (no Authorization header)            -> 401
  POST /box/lifecycle {"action":"bogus"} -> 400 {"error":"Unknown action"}
  GET  /box/tree?user=gabriel          -> 200 {"tree":{"name":"~",...}}
  PUT  /box/file {"path":"spoon-test.txt","content":"hi from task4"} -> 200 {"success":true}
  GET  /box/file?path=spoon-test.txt   -> 200 {"path":...,"content":"hi from task4"}
  GET  /box/file?path=../../../../../etc/passwd -> 400 {"error":"Refusing to access path outside home: ..."}
  GET  /box/status after escape        -> 200 (no crash)
  GET  /box/other?user=gabriel         -> 404 {"error":"Not found"}

apps/agent-worker/src/server.ts

@@ -3,6 +3,15 @@ import type { IncomingMessage, ServerResponse } from 'node:http';
 
 import type { Id } from '@spoon/backend/convex/_generated/dataModel.js';
 
+import {
+  getBoxStatus,
+  listBoxTree,
+  readBoxFile,
+  restartBox,
+  startBox,
+  stopBox,
+  writeBoxFile,
+} from './box';
 import { env } from './env';
 import { attachTerminalServer } from './terminal';
 import {
@@ -56,6 +65,11 @@ const jobRoute = (pathname: string) => {
   return { jobId: decodeURIComponent(match[1]), action: match[2] };
 };
 
+export const boxRoute = (pathname: string) => {
+  const match = /^\/box\/(status|lifecycle|tree|file)$/.exec(pathname);
+  return match?.[1] ? { action: match[1] } : null;
+};
+
 export const startWorkerServer = () => {
   const server = createServer((request, response) => {
     void (async () => {
@@ -73,6 +87,59 @@ export const startWorkerServer = () => {
           sendJson(response, 200, await cleanupOrphanedWorkspaces());
           return;
         }
+        const box = boxRoute(url.pathname);
+        if (box) {
+          const user = url.searchParams.get('user') ?? '';
+          if (!user) {
+            sendJson(response, 400, { error: 'Missing user' });
+            return;
+          }
+          if (request.method === 'GET' && box.action === 'status') {
+            sendJson(response, 200, { status: await getBoxStatus(user) });
+            return;
+          }
+          if (request.method === 'POST' && box.action === 'lifecycle') {
+            const body = await parseJson<{ action?: string }>(request);
+            if (body.action === 'start') {
+              await startBox(user);
+            } else if (body.action === 'stop') {
+              await stopBox(user);
+            } else if (body.action === 'restart') {
+              await restartBox(user);
+            } else {
+              sendJson(response, 400, { error: 'Unknown action' });
+              return;
+            }
+            sendJson(response, 200, { status: await getBoxStatus(user) });
+            return;
+          }
+          if (request.method === 'GET' && box.action === 'tree') {
+            sendJson(response, 200, { tree: await listBoxTree(user) });
+            return;
+          }
+          if (request.method === 'GET' && box.action === 'file') {
+            const filePath = url.searchParams.get('path') ?? '';
+            sendJson(response, 200, {
+              path: filePath,
+              content: await readBoxFile(user, filePath),
+            });
+            return;
+          }
+          if (request.method === 'PUT' && box.action === 'file') {
+            const body = await parseJson<{ path?: string; content?: string }>(
+              request,
+            );
+            sendJson(
+              response,
+              200,
+              await writeBoxFile(user, body.path ?? '', body.content ?? ''),
+            );
+            return;
+          }
+          sendJson(response, 404, { error: 'Not found' });
+          return;
+        }
+
         const route = jobRoute(url.pathname);
         if (!route) {
           sendJson(response, 404, { error: 'Not found' });
@@ -175,9 +242,11 @@ export const startWorkerServer = () => {
         const status =
           message === 'Unauthorized'
             ? 401
-            : message.includes('not supported')
-              ? 409
-              : 500;
+            : message.startsWith('Refusing to')
+              ? 400
+              : message.includes('not supported')
+                ? 409
+                : 500;
         sendJson(response, status, {
           error: message,
         });