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.lock

@@ -6664,15 +6664,6 @@ dependencies = [
  "uuid",
 ]
 
-[[package]]
-name = "solitaire_gpgs"
-version = "0.1.0"
-dependencies = [
- "async-trait",
- "solitaire_data",
- "solitaire_sync",
-]
-
 [[package]]
 name = "solitaire_server"
 version = "0.1.0"