Edit: The problem somehow resolved itself today. I'm not sure how, but I suspect it is because I restarted the computer. I don't believe granting Finder.app full disk access was needed, since I undid that yesterday.
Original post: I can't change icons on APFS-formatted external drive volumes. I've tried many things as detailed below, but nothing is working for me as demonstrated by the screen recording below (click for higher quality): In the screen recording you see that I'm able to change the icon on "old Mac Pro" which is an external volume formatted as Mac OS Extended Journal (using the usual procedure: pasting an image into the upper left of the Get Info). However, the same procedure does not work on the APFS formatted volume, regardless of whether I copy/paste or drag either .png or .icns formatted images.
I've tried this on both a 2015 MacBook Pro and a 2020 M1 MacAir, both running Mac OS 11.3.
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Details of what I've tried: This site says .icns files are required sometimes (since Catalina). This site describes making .icns files using Preview (I found this works for icons when images are 512x512). This video shows making .icns files using a automator quick action found here. User BOrax on this site suggests a need to grant Finder.app full disk access, which I tried using System>Security>Privacy>Full Disk Access> hit + then navigating to /System/Library/CoreServices/Finder.app -- again, nothing helps.
ls -al /Volumes/APFS | grep ".VolumeIcon.icns"
.VolumeIcon.icns -> System/Volumes/Data/.VolumeIcon.icns
, not the icon image itself. You should be able to achieve this from either you HFS+ volume, or from the Recovery volume, i.e. from anywhere that lets you write to the system volume.