Making App Icons on Dock, consistent with the App Icons on Launcher

### Feature Description

I am curious as to if there is a way to make these two consistent without changing `.desktop` files. Some stuff replaces these often or in the case of NixOS, completely locked out via the nature of how immutable works there. It would make sense that if you change an icon on say `Tonearm` to the icon `Gapless` has, it should be consistent on both the regular and bar widget docks.

### Use Case

_No response_

### Compositor(s)

All compositors

### If Other, please specify

_No response_

### Proposed Solution

_No response_

### Alternatives/Existing Solutions

_No response_

No files, tests, or entry points are named. Start by tracing how the launcher and the regular and bar widget docks resolve app icons, then compare their current sources and how icon changes can avoid editing .desktop files. Done means a changed app icon appears consistently in the launcher and both docks across the supported compositors.

Written by the indexing model from the issue text.