feat(sagi): spawn a real claude session for Sagi's Ask handoff

Unmatched Ask questions now adopt a dedicated "Sagi" lane (POST
/api/lanes/ensure, cwd defaults to $HOME) and spawn a tmux-backed claude
run there instead of just prefilling the Run page composer.

client/src/lib/api.ts

@@ -1832,10 +1832,12 @@ export const api = {
     list: () => request<{ lanes: Lane[]; counts: LaneCounts }>("/lanes"),
     /**
      * POST /api/lanes/ensure — ensure a lane exists for the given cwd.
-     * @param body The cwd and optional title.
+     * @param body The cwd and optional title. When `cwd` is omitted the server
+     *   falls back to the user's home directory — useful for lanes whose
+     *   location isn't tied to a specific project (e.g. Sagi's mascot lane).
      * @returns `{ lane, created }` — the lane (newly created or existing) and whether it was created.
      */
-    ensure: (body: { cwd: string; title?: string; pipeline?: string }) =>
+    ensure: (body: { cwd?: string; title?: string; pipeline?: string }) =>
       request<{ lane: Lane; created: boolean }>("/lanes/ensure", {
         method: "POST",
         body: JSON.stringify(body),