a stop button on running background jobs

Killing a job meant asking the agent in words — a whole turn to say "please stop
that", and only possible while the agent is responsive. Now it is a button on the
chip.

── Finding the process ──

The platform does not own these processes. Claude Code starts them and nothing
records a pid. What it has is the file the job streams into, and the job is still
holding that file open — so `fuser` gives the pid, and the file is resolved
through the SAME scoped lookup the read path already uses: the id is validated
against TASK_ID_RE, then matched only under this caller's own directories. An id
that resolves to nothing kills nothing.

Verified end to end rather than reasoned about: a stand-in job holding its output
file open, `fuser` finding it, `{"stopped":true}`, process gone.

SIGTERM, not SIGKILL — a dev server with children should get the chance to take
them down with it. SIGKILL orphans them and leaves the port bound, which is worse
than a stop that takes a second.

── Two things it deliberately does not do ──

It does not dismiss the chip or write a `stopped` status locally. The real end
arrives the way every other end does — the harness sees the exit and the
transcript gets the row — so faking it would be a guess that usually agrees with
reality and sometimes does not. A stop that fails leaves the chip running, which
is the truth.

It does not offer to stop a SUBAGENT. Those write a `.jsonl` transcript rather
than holding a log open, so there is no fd to trace; it says so instead of
pretending.

`Square`, not `X`. X on the same chip means "close this", and confusing "hide the
chip" with "kill the process" is the one mistake worth designing out — which is
why stop appears only on running tasks and dismiss only on finished ones.

tsgo clean, frontend builds, 851 pass / 7 fail unchanged.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/servers/api/chat/chat.ts

@@ -11,6 +11,7 @@ import {
   deleteClaudeSession,
   renameClaudeSession,
   loadBackgroundTask,
+  stopBackgroundTask,
   claudeSessionContext,
   liveSessionTitle,
 } from './claude-sessions';
@@ -270,6 +271,16 @@ chatRouter.get('/tasks/:id', async (ctx) => {
   return ctx.json(detail ?? { kind: 'pending' });
 });
 
+// DELETE /chat/tasks/:id — stop a running background job.
+//
+// Exists so a job can be stopped by pressing a button rather than by asking the agent in words: a turn to
+// say "please stop that" is a turn, and it only works while the agent is responsive.
+chatRouter.delete('/tasks/:id', async (ctx) => {
+  const who = await chatIdentity(ctx.get('user'));
+  const result = await stopBackgroundTask(who, ctx.req.param('id'));
+  return ctx.json(result, result.stopped ? 200 : 400);
+});
+
 // GET /chat/models — Claude tiers only (the runner is the `claude` CLI).
 chatRouter.get('/models', async (ctx: Context) => {
   const who = await chatIdentity(ctx.get('user'));