I'm on Catalina and I want to download Garageband. I get the message that I need Version 11 or later. So I go to Big Sur but my Mac is telling me that no updates are available. Can anyone help?

See instructions in: How to upgrade to macOS Big Sur - Apple Support

It won't allow to download macOS Big Sur and also says can't download newest garageband, download compatible version...and then nothing happens and the question keeps popping up again and again. No software updates available in my system preferences either. Sometimes garageband will open, then sometimes it says update, does the loop of not letting me update or even open.

Is your Mac capable of running Big Sur? See the article linked by FoxFifth to determine if you can.

If so, there are instructions in that article on how to get Big Sur from the App Store.

If you cannot run Big Sur on that Mac, you will also not be able to run that new version of GarageBand.