Hi rejohnson!
The OS of the site server and remote SUP should indeed match for day to day operations, as the site server uses the WSUS management tools to manage the remote WSUS instance, however, it is fine if these mismatch briefly during your upgrade process. I'd still recommend doing them on the same day and disable your SUP sync schedule during the process. As for removing the roles, you can do that at any time before upgrading the SUP.
As for upgrading SQL, you will need to do things in a specific order. Ensure that SQL 2012 is updated to SP4, then the OS can be upgraded to 2019, and finally SQL can then be upgraded to 2019. SQL 2012 SP4 is supported on Server 2019, so you can start there and get the OS upgraded, but I highly recommend not waiting long, as I'm sure you're aware that SQL 2012 is already end of life.
-Anthony