I don't have Topaz Denoise, but I do have Adjust AI and Sharpen AI which both work in Elements 2021.
The Topaz installer creates a plug-in for both 32 and 64 bit operating systems and I think it sometimes gets confused as to which file should be installed in Elements. So, look for the Denoise plug-in file which should have a file extension of .8bf. It will probably be in a location similar to the following:
Make sure you choose the folder with x64 in the name. The denoise plug-in must also have x64 in the name. The Sharpen plug-in is named: tltopazsharpenaips_x64.8bf so I'm guessing that you are looking for a file called tltopazdenoiseaips_x64.8bf
Copy this plug-in file to the following directory: C:\Program Files\Adobe\Photoshop Elements 2020\Required\Plug-Ins\
It should then show up under the Filters menu in the Elements 2020 Editor.
[Edited to reflect the correct path for Elements 2020. I just added the plug-in to my 2020 installation. Obviously, the Topaz installer did not find it by itself.]