Clean up previous implementations

removed:
- catchUpMode and its CATCH_UP_ENTER/EXIT thresholds in ClientGameRunner
- tick metrics fields and overlay UI for inCatchUpMode and beatsPerFrame
- leftover worker heartbeat plumbing (message type + WorkerClient.sendHeartbeat) that was no longer used after self-clocking

changed:
- backlog tracking: keep serverTurnHighWater / lastProcessedTick / backlogTurns, but simplify it to just compute backlog and a backlogGrowing flag instead of driving a dedicated catch-up mode
- frame skip: adaptRenderFrequency now only increases renderEveryN when backlog > 0 and still growing; when backlog is stable/shrinking or zero, it decays renderEveryN back toward 1
- render loop: uses the backlog-aware renderEveryN unconditionally (no catch-up flag), and resets skipping completely when backlog reaches 0
- metrics/overlay: TickMetricsEvent now carries backlogTurns and renderEveryN; the performance overlay displays backlog and current “render every N frames” but no longer mentions catch-up or heartbeats

Learnings during branch development leading to this

Once the worker self-clocks, a separate “catch-up mode” and beats-per-frame knob don’t add real control; they just complicate the model.
Backlog is still a valuable signal, but it’s more effective as a quantitative input (backlog size and whether it’s growing) than as a boolean mode toggle.
Frame skipping should be driven by actual backlog pressure plus frame cost: throttle only while backlog is growing and frames are heavy, and automatically relax back to full-rate rendering once the simulation catches up.

src/client/InputHandler.ts

@@ -131,10 +131,7 @@ export class TickMetricsEvent implements GameEvent {
     public readonly tickDelay?: number,
     // Number of turns the client is behind the server (if known)
     public readonly backlogTurns?: number,
-    // Whether the client is currently in catch-up mode
-    public readonly inCatchUpMode?: boolean,
     public readonly renderEveryN?: number,
-    public readonly beatsPerFrame?: number,
   ) {}
 }