[bugfix] keep track of current tray icon state

[AlexanderYastrebov]

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• I have searched existing issues and pull requests (including closed ones) to ensure this isn't a duplicate
• I have read CONTRIBUTING.md

If this is a feature or change that was previously closed/rejected:

• I have explained in the description below why this should be reconsidered
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Human Written Description

Callers of update_tray_menu previusly required to pass tray icon state which in case of "model-state-changed" listener resulted in a bug that menu was reset to idle when transcription started for the first time.

This change stores tray item state in the app and modifies update_tray_menu to use it such that callers do not need to pass the state.

Related Issues/Discussions

Fixes #
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Testing

Screenshots/Videos (if applicable)

Running transcription for the first time resulted in idle-state menu:

After the fix:

AI Assistance

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If AI was used:

• Tools used: Copilot with Claude Sonnet 4.6
• How extensively: debugging, explain rust copy/borrowing semantics