I'm running Lite 15.3. Do I break anything by upgrading to Python3.7 from 3.6.9?
I am running Zorin 16 beta and my python version (default) is 3.8.10.
I think when you upgrade to Zorin 16, you should be getting a newer version of Python.
As for upgrading in Zorin 15,3, I think it should not break your setup. But you might want to confirm it with other volunteers on this forum.
From my experience, upgrading Python 3 to another point version was done without any issue.
(But when I upgraded Python 2 to 3 in Ubuntu, it was a utterly a nightmare )
I wouldn't think so.
But, if it creates problems, you can Downgrade a package by specifying the lower package number. In your case, you could downgrade back to the original version with
sudo apt install python=3.6.9