fix(anime): honor the sidecar readiness deadline and confirm shutdown

The capabilities probe used a fixed 5s timeout, so a readiness budget
shorter than that could be overrun by one stalled request. Pass the
remaining deadline down instead.

stop() also resolved after the SIGKILL wait even when the child had not
exited, letting a restart race a process still holding the port. Throw
in that case, and keep a failed shutdown from masking the readiness
error at startup.

src/anime-bridge/bridge-client.test.ts

@@ -55,6 +55,20 @@ test('isReady requires every capability the client depends on', async () => {
   assert.equal(await partial.isReady(), false);
 });
 
+test('isReady caps the probe at the deadline the caller passes', async () => {
+  // A bridge that accepts the socket and then stalls: only the abort ends it.
+  const fetchImpl = (async (_input: RequestInfo | URL, init?: RequestInit) => {
+    await new Promise((resolve) => init?.signal?.addEventListener('abort', resolve));
+    throw new Error('aborted');
+  }) as typeof fetch;
+  const client = new AnimeBridgeClient({ baseUrl: 'http://127.0.0.1:9', fetchImpl });
+
+  const started = Date.now();
+  assert.equal(await client.isReady(50), false);
+  // Well under the 5s default, so the per-call deadline is what applied.
+  assert.ok(Date.now() - started < 1000, 'probe outlived the caller deadline');
+});
+
 test('isReady reports false instead of throwing when the bridge is down', async () => {
   const client = new AnimeBridgeClient({
     baseUrl: 'http://127.0.0.1:9',