fix(doctor): add timeouts to subprocess spawns to prevent exit code 137

Doctor checks spawned subprocesses (gh, opencode, sg) without timeouts,
causing the process to hang indefinitely if any binary was stuck.
The OS would then SIGKILL the process (exit code 137).

- Add spawnWithTimeout utility with 10s per-spawn timeout
- Add 30s overall doctor command timeout with graceful error message
- Update all doctor check subprocess calls to use timeouts

src/cli/doctor/spawn-with-timeout.ts

@@ -0,0 +1,36 @@
+import type { SpawnOptions } from "../../shared/spawn-with-windows-hide"
+import { spawnWithWindowsHide } from "../../shared/spawn-with-windows-hide"
+
+const DEFAULT_SPAWN_TIMEOUT_MS = 10_000
+
+export async function spawnWithTimeout(
+  command: string[],
+  options: SpawnOptions,
+  timeoutMs: number = DEFAULT_SPAWN_TIMEOUT_MS
+): Promise<{ stdout: string; exitCode: number; timedOut: boolean }> {
+  let proc: ReturnType<typeof spawnWithWindowsHide>
+  try {
+    proc = spawnWithWindowsHide(command, options)
+  } catch {
+    return { stdout: "", exitCode: 1, timedOut: false }
+  }
+
+  const timeoutPromise = new Promise<"timeout">((resolve) => {
+    setTimeout(() => resolve("timeout"), timeoutMs)
+  })
+
+  const processPromise = (async (): Promise<"done"> => {
+    await proc.exited
+    return "done"
+  })()
+
+  const race = await Promise.race([processPromise, timeoutPromise])
+
+  if (race === "timeout") {
+    proc.kill("SIGTERM")
+    return { stdout: "", exitCode: 1, timedOut: true }
+  }
+
+  const stdout = proc.stdout ? await new Response(proc.stdout).text() : ""
+  return { stdout, exitCode: proc.exitCode ?? 1, timedOut: false }
+}