Unable to add cover art

I'm using MP3TAG v2.97 on Windows 10
The problem occurs with some mp3 files that do not show cover art in MP3TAG and after copying to my smartphone with Google Play Music.
The cover art is visible in Windows Media Player and in File Explorer.
The TagID is ID3v2.3 for all my MP3 files
Add Cover using MP3TAG does not work. The size of the jpg file is 12 KB

The search in this forum with the keywords "google play cover" would have shown you this thread:

Does that help?

Initially i added the coverart with WMP on Windows 10. For most mp3 files it is working ok, except for some. Adding coverart to these MP3 files with MP3TAG does not work. As explained : WMP and File Explorer show the coverart. So, maybe the cover art is embedded somewhere else ?

As an experiment i used MP3TAG to remove coverart from a MP3 file that shows coverart in Play Music and added the coverart again and that works fine

WMP is no tagging program.
Could you apply the following filter and see if the covers are really embedded in the files:
%_covers% MISSING
This should show no files.
All files that show up do not have embedded covers.

Yes, the files that i mention do show up after applying the filter. So, the issue is : why can i not add the cover using MP3TAG

Hard to say, as I cannot look over your shoulder. So I don't know whether it is a handling problem or something with the files.
So how do you try to embed the covers?
The files could be in a format that does not support covers. So what format are they?
The settings to read, write and delete tags could be inconsistent so that you write tags that you don't read - see Tools>Options>Tags>Mpeg for that with special attention to the settings for APE tags.
The files could be corrupt, see How to check files for errors? for tools to check MP3 files.