Add show tray icon setting

[vimtor]

Allow hiding system tray icon via Settings > Advanced. When hidden, closing window quits app instead of hiding.

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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
• I have gathered community feedback (link to discussion below)

Human Written Description

my menu bar gets very cluttered and i needed a setting to hide Handy since i don't use the tray icon that much

Related Issues/Discussions

Discussion: #501

Community Feedback

Discussion: #501

Testing

besides the video below showing the core functionality, i've also tested:

1. closing the settings window, which quits Handy completly if the tray icon is hidden
2. if start hidden is true and show tray icon is false, launching the app from spotlight opens the settings window

⚠️ i've not tested this on a windows or linux machine

Screenshots/Videos (if applicable)

CleanShot.2026-01-25.at.18.09.48.mp4

AI Assistance

• No AI was used in this PR
• AI was used (please describe below)

If AI was used:

• Tools used: Claude Code
• How extensively: Completetly