feat(docker): make the container field a picker you can also type into

Typing a container name from memory is error-prone. The field becomes a native
datalist: pick from the engine's containers, type to filter, or type a name that
is not listed (the engine may be remote, or the container may not exist yet).
A datalist gives all three natively, so no dropdown state machine is introduced.

Adds listDockerContainers and GET /api/docker-hosts/:hostId/containers, following
the listRemoteCodemanSessions discovery precedent: read-only and never throwing,
so an unreachable daemon returns an empty list and the field degrades to plain
text instead of erroring.

Stopped containers stay in the list, sorted after running ones and labelled.
Attaching does require a running container, but hiding stopped ones turns "my
container is not in the list" into a dead end, while showing
`Exited (137) 8 days ago` says exactly what to fix.

src/docker-hosts.ts

@@ -1049,6 +1049,55 @@ export interface AdoptedContainerProbe {
   error?: string;
 }
 
+/** One container on the engine, as offered to the adoption picker. */
+export interface DockerContainerInfo {
+  name: string;
+  image: string;
+  running: boolean;
+  /** Engine's own status string, e.g. "Up 3 hours" / "Exited (0) 2 days ago". */
+  status: string;
+}
+
+/**
+ * List the engine's containers for the adoption picker (mirror of
+ * `listRemoteCodemanSessions`). Read-only and NEVER throws: an unreachable
+ * daemon, a missing engine or zero containers all return `[]`, because this
+ * feeds a convenience picker whose input the user can always type by hand.
+ *
+ * Stopped containers ARE included, sorted after running ones and carrying their
+ * status: adoption requires a running container, but hiding a stopped one turns
+ * "my container is not in the list" into a dead end with no explanation, while
+ * showing `my-box (Exited (0) 2 days ago)` says exactly what to fix.
+ */
+export async function listDockerContainers(
+  docker: Pick<SessionDocker, 'engine' | 'context' | 'daemonHost'>
+): Promise<DockerContainerInfo[]> {
+  if (IS_TEST_MODE) return [];
+  const argv = dockerEngineArgv(docker);
+  try {
+    const { stdout } = await execFileAsync(
+      argv[0],
+      [...argv.slice(1), 'ps', '-a', '--format', '{{.Names}}\t{{.Image}}\t{{.State}}\t{{.Status}}'],
+      { timeout: DOCKER_PROBE_TIMEOUT_MS }
+    );
+    const rows = stdout
+      .split('\n')
+      .map((line) => line.split('\t'))
+      .filter((parts) => parts.length >= 4 && parts[0])
+      .map(([name, image, state, status]) => ({
+        name,
+        image: image || '',
+        running: state === 'running',
+        status: status || '',
+      }));
+    // Running first, then by name, so the containers a user can actually adopt
+    // are the ones at the top of the list.
+    return rows.sort((a, b) => Number(b.running) - Number(a.running) || a.name.localeCompare(b.name));
+  } catch {
+    return [];
+  }
+}
+
 /**
  * Preflight an EXISTING container for adoption. Read-only by construction: it
  * runs `inspect` plus one `exec` of `command -v`, and never creates, starts or