Saw that other users had the same problem as me, trying to change the avatar on the iOS app (signed in with AppleID).
None of the suggested solutions worked, but I stumbled on a way to do so.
Sharing screenshots here.
The key step seems to be logging out of the iOS app first. Only then can the avatar be changed.
Hope this helps others...
@Sukanta_Biswas
@Crazy Cat Lad