feat: store launcher state outside game dirs

Move launcher-owned metadata from game roots into the configured peer state
area. Peer identity, the local library index, install intent logs, and setup
markers now live under app/CLI state instead of being written beside games.
The Tauri shell passes its app data directory into the peer, and the peer CLI
runs the same path through its explicit --state-dir.

Add a dedicated pre-start migration phase for legacy files. It migrates the
old global library index, per-game install intents, and the old first-start
marker into app state, then deletes legacy files only after the replacement
write succeeds. Normal scan, install, recovery, and transfer paths no longer
read legacy state files.

Rename the old first-start meaning to setup_done and only set it after
launching game_setup.cmd. Start/setup scripts keep the shared argument shape,
while server_start.cmd now uses cmd /k and a visible window so server logs stay
open for inspection.

While validating the Docker scenario matrix, make download terminal events
come from the handler after local state refresh and operation cleanup. This
makes download-finished/download-failed safe points for immediate follow-up CLI
commands. Also update the multi-peer chunking scenario to use a sparse archive
large enough to actually span multiple production chunks.

Test Plan:
- just fmt
- just test
- just frontend-test
- just build
- just clippy
- git diff --check
- python3 crates/lanspread-peer-cli/scripts/run_extended_scenarios.py

Refs: local app-state migration discussion

IMPL_DECISIONS.md

@@ -5,9 +5,10 @@
   directly.
 - Renamed the frontend success event to `game-install-finished`; the old
   unpack name no longer matched the transactional install/update lifecycle.
-- Implemented watcher rescans by reusing the existing `.lanspread/library_index.json`
-  cache and updating a single game entry in that index. This satisfies the
-  per-ID optimized rescan requirement without adding a second cache format.
+- Implemented watcher rescans by reusing the app-state
+  `local_library/index.json` cache and updating a single game entry in that
+  index. This satisfies the per-ID optimized rescan requirement without adding a
+  second cache format.
 - Split full startup recovery from ordinary settled refreshes. Startup and real
   `SetGameDir` changes run recovery plus a scan; install/update/uninstall
   completion only rescans the affected game after operation tracking has been