[Feature Request] API to control Command Palette Dock background color and theme

### Description of the new feature / enhancement

Please allow controlling the background color and theme of the Command Palette Dock through an API.
By doing so, we can dynamically change its appearance to match the current foreground application, achieving an immersive Command Palette Dock experience.

### Scenario when this would be used?

When users switch between different applications, third-party customization tools or scripts can use this API to sync the Command Palette Dock's theme and background color with the active foreground window. This provides a visually unified and immersive desktop environment.

### Supporting information

N/A

No files, tests, or entry points are mentioned. Start by locating the Command Palette Dock implementation and its existing customization or API surface, then determine the supported contract for controlling background color and theme. Done means a usable API can update both properties and the behavior is covered by appropriate tests or documented validation.

Written by the indexing model from the issue text.