Garage Band / Logic Pro for Catalina

Do you already own a copy pf GarageBand or Logic ? If these apps are in your Purchase History at the AppStore, try to download them from the Purchase history. Then the Appstore might offer you to download an older version, compatible with your current system.

I am still seeing Logic Pro and GarageBand even on my older Macs with macOS 10.14 Mojave, but only, when I look at my Purchase History.

Logic is an expensive separate Purchase. You may have purchased it preinstalled, but id´f you ever updated it at the AppStore, it should be associated with your Apple ID.

If you had GarageBand 10 preinstalled on your Mac, you should have seen a prompt at the AppStore to accept GarageBand to associate it with your AppleID. then you can download it from the Purchases history.

If you only had the older GarageBand '11, it would not help. GarageBand '11 has been deprecated and cannot be updated to run on Catalina.

No , those apps requires a macOS 14 or later