[some apps won't let me select photos from Gallery, only Camera]

[B. Diddy]

Show us a screenshot of the selection screen in iOS Launcher 14 when you choose the Change Icon option, just so I can see if it's the same one I looked at.

 

[ghostlyx]

Here it is.
This is also the last post for now, I'm going to bed

 

[Laura Knotek]

What happens if you use the stock OneUI launcher? I'm thinking that your issue is related to the launcher you're using.

 

[B. Diddy]

I agree with Laura Knotek -- this is probably some issue with how the particular apps are coded. Send feedback to those developers about it.