Stumbled over this post and ran into the same issues that other users have mentioned when running macOS Catalina 10.15.
After running the debug I saw a duplicate error showing a missing directory, so as an experiment, I ran the following in Terminal:
mkdir ~/Library/Caches/com.runningwithcrayons.Alfred-3/ && mkdir ~/Library/Caches/com.runningwithcrayons.Alfred-3/Workflow\ Data/
This created the directory where the python script returns album thumbnails from the Album & Song search commands.
Additionally since Catalina replaces iTunes.app with Music.app, I went through the three python scripts and archived some of the URL scheme that Music doesn't seem to need. I bumped up the workflow version to 2.1 for tracking purposes.
Search Apple Music.alfredworkflow [Google Drive]
Thanks to all the creators who have put this together!
Pro-Tip: Update Line 19/20 in the artist, album, and song python scripts to your country code to improve search results with images.