Everything can be done as a single (but often quite long) command, something like this:

for filepath in A/*; do filename=$(basename "$filepath"); name="${filename%.*}; match=$(ls B/"$name".* 2>/dev/null); [ -z "$match" ] && rm "$filepath"; done

What it does is

1. Loops over the files in directory A
2. Gets the filename (my_file.ext)
3. Strips the extension
4. Looks for any files in B with the same name but any extension
5. If no match, delete the file (from A)
   I haven’t tested it so might be some typos in there, also maybe replace rm with echo and run it first just to see what files it would have deleted, there’s no undo when you use rm

I believe comm is your friend here. Something like get the contents of both directories, strip the suffix, sort, pass both lists to comm, re-add the extension, and delete those files.

Does one of the diff options in this discussion help to generate the list of files? I’m limited to a phone for a few days, but I can test them later.