fix: reuse shared connection status components in PlayGameEngine

[Hakimi674]

Overview

This PR removes the hand-rolled connection-status UI in PlayGameEngine and wires in the existing shared components (ReconnectionBanner and ConnectionStatusIndicator), consolidating the duplicated implementation into a single source of truth.

Related Issue

Changes

🔌 Connection Status Consolidation

• [MODIFY] frontend/components/chess/PlayGameEngine.tsx

  • Removed the inline socketStatusLabel() rendering (previously at lines 323-345).
  • Now renders the shared ConnectionStatusIndicator for the compact status display and ReconnectionBanner for the reconnection notice.

• [MODIFY] frontend/components/ReconnectionBanner.tsx

  • Adjusted so it can be consumed by PlayGameEngine (props/rendering aligned with the engine's connection state).

• [MODIFY] frontend/components/chess/ConnectionStatusIndicator.tsx

  • Adjusted so it can be consumed by PlayGameEngine (props/rendering aligned with the engine's connection state).

Verification Results

Manual check:
✅ PlayGameEngine renders shared ConnectionStatusIndicator instead of socketStatusLabel()
✅ ReconnectionBanner displays on disconnect/reconnect flow
✅ No remaining hand-rolled connection-status markup in PlayGameEngine

Acceptance Criteria	Status
Use the shared components in PlayGameEngine (and the home page online bar)	✅ PlayGameEngine now uses ReconnectionBanner + ConnectionStatusIndicator
Delete whichever implementation is not kept	✅ Inline socketStatusLabel() UI removed from PlayGameEngine

Closes #1366

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