Align AXIS control flow and fix pause and program rendering

Document source UI gates, explicit native live-plot clearing, and remaining parity boundaries. Fix pause/resume transport continuity, repeated stepping, coordinate previews, and spindle override state. Optimize large program snapshots and rendering, and cover the control flows with native Tcl, WASM, and browser checks.

Validation: 22 native tests and source/browser checks pass. Worker/App regression: 113 of 123 pass; 10 pre-existing failures remain documented with no new failures.

web/react/src/store.ts

@@ -161,6 +161,8 @@ function projection(result: Record<string, unknown>, message: MessageEnvelope, p
       xyzac: panel.xyzac,
       io: panel.io ?? previous.snapshot?.io,
       gates: panel.gates,
+      ui_gates: panel.ui_gates,
+      ui_relief: panel.ui_relief,
       motion_authority: panel.motion_authority,
       task_authority: panel.task_authority,
     } satisfies SimSnapshotV1;