Decouple pause from the game server

The game server tracks whether the game is paused in order to stop spawning GameFrame packets during pause. Make it so that it doesn't need to track pause. This likely involves making it send frame packets indiscriminately and making sure clients handle it correctly (gameframe packets largely ignored during pause; no skips in frame number from client PoV, probably a locally kept offset; replays work correcty).

No files, tests, or entry points are named. Trace how the game server tracks pause and emits GameFrame packets, then inspect client pause handling and replay behavior; done means the server no longer tracks pause while clients preserve frame numbering, ignore paused frames appropriately, and replays remain correct.

Written by the indexing model from the issue text.