### PlayerWebSocketHandler updates
- Track `ticket` and `match_id` per player instance
- Handle `matchmaker_ticket` messages and store ticket
- Handle `matchmaker_matched` and automatically join created match
- Enhance matchmaking debug output
- Update join_matchmaking() to include mode-based string_properties + query
### Matchmaking simulation improvements
- Evenly distribute players between "classic" and "blitz" modes
- Randomize assignment order to simulate real queue behavior
- Log player→mode mapping for visibility during tests
Example:
player_0 -> classic
player_3 -> blitz
player_5 -> classic
Client test harness now accurately reflects multi-mode matchmaking behavior.
### Summary
Replaced legacy RPC-based matchmaking flow with proper WebSocket-driven
matchmaker integration. Player simulation now queues via
`matchmaker_add`, auto-joins matches on `matchmaker_matched`, and no
longer depends on `rpc_find_match`.
