[S4.1-09] UX Loading and Error Polish Pass (Game + Admin + Stats)

Labels: stage-4, frontend, ux
Depends on: S4.1-08

Acceptance Criteria:

- [ ]  Core screens have explicit loading states.
- [ ]  User-facing error messages are actionable and consistent.
- [ ]  Retry actions exist for recoverable network failures.
- [ ]  No dead-end states remain in normal user flows.