How can I change the disk icon on 2 USB external drives (APFS format) on a Mac mini?

I usually use custom drive icons that I have collected over the years.

Control-click the icon of a drive whose icon you want to copy. Select GetInfo. Then single-click the small disk icon in the upper left of the GetInfo panel in order to select it. Then do CMD-C (or Edit > Copy) to copy the icon to the clipboard.

Then do GetInfo on the drive whose icon you want to change. Single-click the small disk icon in the upper left of the GetInfo panel. Then do CMD-V (or Edit > Paste) top copy the icon to the new drive.

see > Change icons for files or folders on Mac - Apple Support

If that's not working..? Restart and try again.

This seems more like a Sonoma 14.4 issue, because I have custom icons set for my APFS formatted internal and external backup drives.

If you can't make it work? Then I suggest sending Feedback to Apple, using > Feedback - macOS - Apple

When, exactly, did this behavior start? Before you updated to 14.4? Immediately after updating? Later?

Have you manually rebooted your Mac any time since completing the update?

Have you tried changing a disk icon in a different user account on the Mac?

Look again, those are all custom icons and not native macOS icons.

I would try Safe Mode followed by a normal Restart, to see if that clears up the problem.

see > Use safe mode on your Mac - Apple Support