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

crates/lanspread-peer/ARCHITECTURE.md

@@ -124,7 +124,8 @@ Reserved per-game paths:
 - `.local.installing/` is extraction staging.
 - `.local.backup/` holds the previous install while an update or uninstall is in
   flight.
-- `.lanspread.json` is the atomic per-game intent log.
+- `games/<game_id>/install_intent.json` in the configured state directory is the
+  atomic per-game intent log.
 - `.lanspread_owned` inside `.local.*` directories proves Lanspread ownership
   when the current intent is `None`.
 
@@ -133,11 +134,17 @@ game root only for a catalog ID that is a single direct child of the configured
 game directory, has a regular root-level `version.ini`, and has no `local/`,
 `.local.installing/`, or `.local.backup/` path.
 
-Recovery reads `.lanspread.json` and combines the recorded intent with the
-observed `local/`, `.local.installing/`, and `.local.backup/` state. Intent
-states `Installing`, `Updating`, and `Uninstalling` prove ownership of the
-corresponding reserved directories even if the marker was not flushed before a
-crash. With intent `None`, markerless `.local.*` directories are left untouched.
+Recovery reads app-state `install_intent.json` and combines the recorded intent
+with the observed `local/`, `.local.installing/`, and `.local.backup/` state.
+Intent states `Installing`, `Updating`, and `Uninstalling` prove ownership of
+the corresponding reserved directories even if the marker was not flushed before
+a crash. With intent `None`, markerless `.local.*` directories are left
+untouched.
+
+Legacy `.lanspread/`, `.lanspread.json`, `.lanspread.json.tmp`,
+`.softlan_game_installed`, and `local/.softlan_first_start_done` files are
+handled only by the dedicated pre-start migration phase. Normal operation does
+not read legacy state paths.
 
 ### Result
 
@@ -195,8 +202,8 @@ Most scans become O(number of game dirs), with full recursion only when needed.
    - Cache the last accepted `manifest_hash` per peer to short-circuit
      manifest requests when unchanged.
 5. Local index + scan optimizations:
-   - Introduce a cached index file (e.g., `.lanspread/index.json`) that stores
-     per-root fingerprints and computed manifests.
+   - Use the cached `local_library/index.json` file in the configured state
+     directory to store per-root fingerprints and computed manifests.
    - Use filesystem watchers with a debounce window to collect changes and
      incrementally update the cache.
    - Schedule a low-frequency full scan to reconcile missed watcher events.