Populate the program stack select from castle-api

The dashboard's stack dropdown hardcoded its options (python-cli/fastapi/
react-vite), so a supabase program showed "(none)" — the value had no matching
option. Make the backend the single source of truth instead:

- core: available_stacks() returns sorted(HANDLERS) — the stacks castle has
  handlers for.
- castle-api: GET /stacks exposes it.
- cli: --stack choices derive from available_stacks() (drops the duplicated list).
- app: ProgramFields fetches /stacks (useStacks) and renders options from it,
  always including the current value so it never silently blanks; StackBadge
  gets a Supabase label.

A new backend stack now appears everywhere without a frontend edit.

castle-api/src/castle_api/programs.py

@@ -4,12 +4,19 @@ from __future__ import annotations
 
 from fastapi import APIRouter, HTTPException, status
 
-from castle_core.stacks import available_actions, run_action
+from castle_core.stacks import available_actions, available_stacks, run_action
 
 from castle_api.config import get_config
 
 programs_router = APIRouter(tags=["programs"])
 
+
+@programs_router.get("/stacks")
+def list_stacks() -> list[str]:
+    """Stack names castle has handlers for — populates the dashboard's stack select
+    and keeps it in sync with the backend (no hardcoded frontend list)."""
+    return available_stacks()
+
 # ---------------------------------------------------------------------------
 # Unified program action endpoint
 # ---------------------------------------------------------------------------