chore(data,engine,docs): remove Google Play Games Services sync backend

Deletes the solitaire_gpgs crate and all GPGS references from settings,
sync client, profile plugin, CLAUDE.md, and ARCHITECTURE.md. The
self-hosted server covers all sync needs without the Android-only backend.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

solitaire_engine/src/profile_plugin.rs

@@ -260,7 +260,6 @@ fn sync_info(backend: &SyncBackend) -> (&'static str, String) {
         SyncBackend::SolitaireServer { username, .. } => {
             ("Solitaire Server", username.clone())
         }
-        SyncBackend::GooglePlayGames => ("Google Play Games", "—".to_string()),
     }
 }