fix(peer): refresh settled install state after operations

The follow-up review found a few stale lifecycle edges around local game
transactions. Recovery could sweep active roots, post-operation refreshes
still re-ran full startup recovery, and the UI kept inferring local-only state
from downloaded and installed flags instead of the backend availability.

This updates the peer lifecycle so startup recovery skips active operations,
install/update/uninstall refresh only the affected game after the operation
guard is dropped, and path-changing game-directory updates are rejected while
operations are active. It also removes the dead UpdateGame command, drops the
unused manifest_hash write field while preserving old JSON reads, renames the
internal install-finished event, and carries availability through the DB,
peer summaries, Tauri refreshes, and the React model.

The included follow-up documents record the review source, implementation
decisions, and the remaining FOLLOW_UP_2.md work so later commits can stay
small instead of reopening the completed plan items.

Test Plan:
- git diff --check
- just fmt
- just clippy
- just test

Follow-up-Plan: FOLLOW_UP_PLAN.md

crates/lanspread-peer/src/lib.rs

@@ -58,7 +58,6 @@ use crate::{
         handle_list_games_command,
         handle_set_game_dir_command,
         handle_uninstall_game_command,
-        handle_update_game_command,
         load_local_library,
     },
 };
@@ -159,8 +158,6 @@ pub enum PeerCommand {
     },
     /// Install already-downloaded archives into `local/`.
     InstallGame { id: String },
-    /// Update an installed game from already-downloaded archives.
-    UpdateGame { id: String },
     /// Remove only the `local/` install for a game.
     UninstallGame { id: String },
     /// Set the local game directory.
@@ -291,9 +288,6 @@ async fn handle_peer_commands(
             PeerCommand::InstallGame { id } => {
                 handle_install_game_command(ctx, tx_notify_ui, id).await;
             }
-            PeerCommand::UpdateGame { id } => {
-                handle_update_game_command(ctx, tx_notify_ui, id).await;
-            }
             PeerCommand::UninstallGame { id } => {
                 handle_uninstall_game_command(ctx, tx_notify_ui, id).await;
             }