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>

Cargo.toml

@@ -5,7 +5,6 @@ members = [
     "solitaire_data",
     "solitaire_engine",
     "solitaire_server",
-    "solitaire_gpgs",
     "solitaire_app",
     "solitaire_assetgen",
 ]