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-proto/src/lib.rs

@@ -7,6 +7,8 @@ pub const PROTOCOL_VERSION: u32 = 2;
 #[derive(Clone, Debug, Serialize, Deserialize, PartialEq, Eq, Hash)]
 pub enum Availability {
     Ready,
+    /// Wire-compatible transitional state. Local library summaries currently
+    /// suppress active operations instead of advertising this value.
     Downloading,
     LocalOnly,
 }