fix(debug): align web/app debug status fields between service and UI

[Asuka22687]

Summary

This PR aligns debug status field naming between backend service and UI to prevent incorrect state branching.

Problem

Service state uses webDebug, while parts of the UI logic read appDebug.

Because of this mismatch, debug-state checks can evaluate incorrectly and launch flow may enter wrong branches.

Root Cause

Field naming diverged over time across:

• service state payload
• client initial state
• websocket event handling

Changes

Service-side compatibility

• Added appDebug alongside webDebug in the service debug state object.
• Kept both fields synchronized during state transitions (connect/disconnect and app launch reset).

UI-side normalization

• Added webDebug to initial context state.
• Normalized incoming debug payload in websocket client:
  • derives both webDebug and appDebug from incoming payload (webDebug || appDebug)
• Updated gating checks to use normalized webDebug path.
• Ensured handleCanLaunchModules updates both fields for compatibility.

Backward Compatibility

Maintains compatibility for both payload shapes:

• old clients expecting appDebug
• current service shape with webDebug

Validation

• Static syntax checks:
  • node --check service index.js
  • node --check service utils/debugger.js
  • node --check UI WebSocketClient.js

Risk

Low to medium. Multi-file change but constrained to debug status mapping/state sync.