I just downgraded from Big Sur to Catalina. Initially I had the same problem. I couldn't download a compatible version from the App Store. But clicking on my name in the bottom left-hand corner to reveal my purchases worked for me. I found GarageBand in my list of purchases and I was able to download a Catalina compatible version. So it's out there! Maybe it's critical that GB shows up in your purchases.
Another suggestion - if you've got GarageBand for Catalina on another Mac (or a friend does), it may be possible to send the app via sharing on iCloud Drive. I was able to do this with MainStage. A friend of mine has High Sierra on his MacBook and wanted to download MainStage for all the extra sounds that gives. No-go from the App Store... I dragged the app to my desktop and sent it to him via iCloud Drive. He's really not so good with computers but was still able to get it up and running...