Have you purchased Logic Pro?
If you have, then all you need to do is select your account at the bottom left of the App Store window, locate Logic Pro amongst your purchases, and click to download. A warning appears, saying the current version is not compatible, and allowing you to download the very last that works in Ventura.
If you haven't purchased, the application, you may do so using a friend's computer, logging in to YOUR Apple ID, deleting the application and then proceeding as described above to download to your computer.
All that said, do you really need Logic Pro on an older computer? Odds are that GarageBand may do all that you need, and is free.