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/remote_peer.rs

@@ -2,7 +2,12 @@
 
 use std::{collections::HashMap, net::SocketAddr, sync::Arc};
 
-use lanspread_db::db::Game;
+use lanspread_db::db::{
+    AVAILABILITY_DOWNLOADING,
+    AVAILABILITY_LOCAL_ONLY,
+    AVAILABILITY_READY,
+    Game,
+};
 use lanspread_proto::{Availability, GameSummary};
 use tokio::sync::RwLock;
 
@@ -26,10 +31,12 @@ pub async fn ensure_peer_id_for_addr(
 }
 
 pub fn summary_from_game(game: &Game) -> GameSummary {
-    let availability = if game.downloaded {
-        Availability::Ready
-    } else {
-        Availability::LocalOnly
+    let availability = match game.availability.as_str() {
+        AVAILABILITY_READY => Availability::Ready,
+        AVAILABILITY_DOWNLOADING => Availability::Downloading,
+        AVAILABILITY_LOCAL_ONLY => Availability::LocalOnly,
+        _ if game.downloaded => Availability::Ready,
+        _ => Availability::LocalOnly,
     };
 
     GameSummary {