local-dev: stop spawned engine containers in down/clean

Backend's runtime spawns the engine container outside the compose
project, so `docker compose down` left a `galaxy-game-…` container
running. Add a `stop-engines` target that finds them by their OCI
image-title label (set in game/Dockerfile) and remove forcibly;
make `down` and `clean` depend on it. `clean` additionally wipes
the per-game state directory under /tmp/galaxy-game-state.

Add a troubleshooting note for the related symptom: when the
browser holds a keypair from a previous DB and `make clean`
recreates everything, the lobby renders "no games yet" until the
user clears site data or opens an incognito window. The dev user
keeps the same email but receives a fresh user_id, which the old
keypair cannot authenticate against.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

tools/local-dev/README.md

@@ -181,6 +181,19 @@ make status         docker compose ps
 
 ## Troubleshooting
 
+- **Lobby shows "no games yet" after `make clean && make up`** —
+  the browser still holds a keypair + device session bound to the
+  user_id from the previous DB. The new user has the same email
+  (`dev@local.test`) but a fresh user_id, so the old keypair
+  authenticates against a session row that no longer exists or
+  points at the wrong account. Open the page in an incognito
+  window, or wipe site data for `localhost:5173` (DevTools →
+  Application → Storage → Clear site data) and log in again.
+- **`make down` leaves a `galaxy-game-…` container behind** — fixed
+  in this Makefile: `make down` and `make clean` now stop spawned
+  engine containers via the `org.opencontainers.image.title=
+  galaxy-game-engine` label. To stop them by hand without touching
+  the rest of the stack, `make stop-engines`.
 - **`make up` reports a build error mentioning `pkg/cronutil`** —
   upstream module list drifted; copy any new `pkg/<name>/` line into
   the local-dev `backend.Dockerfile` / `gateway.Dockerfile` to match