Process for upgrading MySQL Master-Slave to a new release series version

I have several MySQL servers that I want to upgrade from 5.7.31 to the most recent release series (5.7.36 I believe), but in one test I found that replication on one server set failed, and it required me to re-import a backup from the primary to recover. I don't see any official documentation from MySQL on how to do this properly. Is there anyone who has done this before with Master-Slave replication, and if so, what steps did you take to make sure you didn't break replication?