Install 20.04 for wsl2 if Microsoft Store is dysfunctional?

As long as you already have WSL installed (which doesn't rely on the Store anyway, so that shouldn't be a problem), you can use the wsl --import subcommand to get the Ubuntu distribution "side-loaded".

The package that you already downloaded contains the file you need, but for the sake of streamlining the directions, I'm going to have you download it again. You can tweak this recipe if you'd like, of course:

• First, choose a location for your WSL files. For example:

  cd $env:USERPROFILE
  mkdir -p wsl\instances\Ubuntu20_04
  mkdir wsl\images
  cd wsl
  

• Download the Appx package manually into that wsl directory, either through the proper direct link found here or, in your case, via:

  # Assuming we are still in the `wsl` directory created above
  Invoke-WebRequest -Uri https://aka.ms/wslubuntu2004 -OutFile Ubuntu.appx -UseBasicParsing 
  

• The resulting file is actually just a renamed .zip file. Extract it in PowerShell and move the install.tar.gz to the images directory created above:

  # Still in the `wsl` directory
  Expand-Archive Ubuntu.appx
  mv Ubuntu\install.tar.gz images\
  Remove-Item -Recurse Ubuntu
  

• You'll need to extract the install.tar.gz file to install.tar. Neither PowerShell nor Windows have a built-in feature to do this, so I'll leave that to your preference. I'm guessing you already have something like 7-zip installed already.

• Rename the images\install.tar to images\Ubuntu20_04.tar. This isn't strictly necessary, but I like to keep the "pristine" image around in case you want to install additional instances. WSL is great for spinning up "throwaway" instances where you can try out something potentially destructive without fear of corrupting your main instance.

• Still from within the wsl directory:

  wsl --import Ubuntu20.04 instances\Ubuntu20_04 images\Ubuntu20_04.tar --version 2
  wsl --set-default Ubuntu20.04 # Optional, and perhaps unnecessary if this is the first distribution installed
  wsl -u root useradd --create-home --user-group --groups  adm,dialout,cdrom,floppy,sudo,audio,dip,video,plugdev,netdev --password "encryptedPassword" username
  

  ... Of course, adjust username to be your username. See here for how to create the encrypted password.

  To the best of my knowledge, this will create a user the same way that the default user is created by the Microsoft Store installation of Ubuntu 20.04.

• Start WSL Ubuntu as root:

  wsl -u root
  

• To set the default user that runs when the instance starts, create a /etc/wsl.conf with the following contents:

  [user]
  default=username
  

  ... substituting your username, of course.

• Exit back to PowerShell

• Shutdown the instance to allow it to come back up and read the wsl.conf:

  wsl --terminate Ubuntu20.04
  

That should be it. Running wsl should start Ubuntu 20.04 running under your user ID.

I haven't had a chance to test every step in here end-to-end, but this is a combination of things I've done in the past and other answers I've provided. I believe I've got all the pieces put together that you need, but if you run into issues, let me know, and I'll review and tweak it.