feat(docker): take run-mode availability from the container

The run-mode dropdown hides CLIs that are not installed on the HOST (#201). That
is right for local sessions and wrong for a container case, whose agents run
inside the container: a host with no claude installed hides the mode while the
container ships one, which is exactly what happened on a real deployment.

The adoption preflight already probes what the container has, so that result is
persisted on the case and surfaced through CaseInfo. Docker cases gate on it;
every other case keeps the host probe unchanged.

An absent list reads as "do not gate" rather than "nothing available": an owned
container runs our base image, which ships every CLI, and treating unknown as
empty would leave the menu with Shell alone.

src/types/api.ts

@@ -167,6 +167,13 @@ export interface CaseInfo {
     image?: string;
     path: string;
     network?: string;
+    /**
+     * CLIs available INSIDE the container. A container case runs its agents in
+     * the container, so HOST CLI availability says nothing about what it can
+     * run. Absent = unknown (an owned container runs our base image, which ships
+     * every CLI), which the UI reads as "do not gate".
+     */
+    availableModes?: string[];
   };
 }
 

src/types/session.ts

@@ -261,6 +261,15 @@ export interface DockerCase {
    * all created by us).
    */
   owned?: boolean;
+  /**
+   * CLIs found INSIDE the container by the adoption preflight. A container case
+   * runs its agents in the container, so host CLI availability says nothing about
+   * what this case can run — the base image ships every CLI, and an adopted
+   * container ships whatever its owner installed. Absent = unknown (owned cases,
+   * or a case linked before this field existed), which callers read as "do not
+   * gate".
+   */
+  availableModes?: SessionMode[];
   /** Last captured Claude conversation id, replayed via --resume on a fresh launch. */
   lastClaudeSessionId?: string;
 }