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

Also if there are 100k+ files this is likely going to be relatively slow, then i would create two files containing the names of all the files in each directory, sort them, then there is a command to find differences between them very efficiently but i don’t remember which…

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.