Automatically move Desktop Widget position based on currently selected wallpaper

### Feature Description

Add an option to somehow save the desktop widget position per wallpaper based. When we change (or randomized) the wallpaper, it will automatically move to the previously saved position for that wallpaper.

### Use Case

Let's say I have a clock widget on the center of the screen. It works fine for wallpaper A, but it doesn't suit for wallpaper B. I have to move the widget everytime I change wallpaper. With this feature, I can change the wallpaper and the widget will automatically move to previously saved position for that selected wallpaper.

### Compositor(s)

All compositors

### If Other, please specify

_No response_

### Proposed Solution

_No response_

### Alternatives/Existing Solutions

_No response_

The issue does not name any files, tests, or entry points to inspect. Clarify how wallpapers are identified, where widget positions should be stored, and how randomized changes are handled before locating the relevant wallpaper and widget-position code. Done should include restoring each widget's saved position for its wallpaper across all listed compositors.

Written by the indexing model from the issue text.