When you purchased MC23, you were emailed a registration code. You were probably also emailed a file that ends in .MJR . That's a licensing file that normally automatically updates the license on your trial version of MC to the licensed version.
In my experience the MJR file doesn't work very consistently on Mac. So I always manually license. The process is VERY EASY.
Find the email with your registration code.
Open MC.
Go to the help menu. You'll see an entry something like "register MC". Click on it.
When it brings up a dialog copy and paste your registration code in.
That should do it. Your copy of MC should now be registered.
If it's not 100% clear: The MC program that you have installed already, which is a "trial version" is actually the full version. It just times out and stops working after a while. Once you license it, it will work forever.
Good luck.
Brian.