XCode Diaries : I installed sonoma over catalina and now can't upgrade to catalina

You’re seemingly confused about your macOS versions.

macOS 10.15 (Catalina) is a while back, and was followed by macOS 11 (Big Sur), macOS 12 (Monterey), macOS 13 (Ventura), and the current macOS 14 (Sonoma).

if you’re running macOS 10.15 and want a recent or current Xcode, yes, you will need to upgrade to macOS 13 or to macOS 14.

Xcode 15.3 requires macOS 14.0 or later.

Xcode 15.2 requires macOS 13.5 or later.

Have a backup of your macOS environment, or minimally a backup of the data that matters.

Upgrade to macOS 13 or macOS 14, as your next step:

How to download and install macOS - Apple Support

Then update macOS:

Update macOS on Mac - Apple Support

Then download Xcode from either the Mac App Store, or from the developer portal. You might need to use the developer portal to get an older version of Xcode, if your Mac cannot be upgraded to macOS 14. If your Mac supports macOS 14, then Xcode 15.3 can be downloaded from either the Mac App Store or the developer portal.

Ignore the macOS marketing names. Those add complexity without adding clarity. Focus on the (full) version numbers.