Keyboard shortcuts don't close to tray

### Steps To Reproduce

1. Go to `File > Settings`
2. Ensure "Close to tray icon" is checked / enabled.
3. Press either `CTRL+Q` (quit) or `CTRL+W` (close) on your keyboard.

### Expected Result

The currently open window should close but the application stay running in the background.

### Actual Result

The application does not stay running in the background.

### Screenshots or Videos

_No response_

### Additional Context

This is an issue for both SSH agent functionality and keeping the vault unlocked.

### Operating System

Linux

### Operating System Version

_No response_

### Installation method

Flatpak

### Build Version

2025.8.2

### Issue Tracking Info

- [x] I understand that work is tracked outside of GitHub. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

Start by reproducing the issue on Linux using the Flatpak build, with “Close to tray icon” enabled and both Ctrl+Q and Ctrl+W. Trace the desktop keyboard shortcut and window-close handling. Done means the window closes while the application remains running in the tray, preserving SSH agent functionality and the unlocked vault.

Written by the indexing model from the issue text.