Upgrade Logic Pro 10.5.1. to Big Sur 11.7.10

Log into the appstore with your appleID and look for Logic. If there is still no update possible, move your Logic.app into the trash, but don't need to empty the trash. Then go back into the AppStore, you may have to log out and log in again.... But please, create a TimeMachine backup before doing anything. Also keep the old Logic version and rename it to e.g. Logic 10-5-1. You can place both Logic versions into the application folder later.

Back up Logic Pro for Mac - Apple Support

The current version of Logic Pro requires macOS 13.5 Ventura or later. Big Sur is the last version of macOS a late 2013 MBP can run, so you will not be able to run the most current release of Logic Pro. If there are any updates to your version, they would appear in your Mac's App Store's Updates section.

Regards.

You are absolutely right, but sometimes you need to trigger the update manually with a procedure similar I've explained in my answer above.