Older versions (5.x) of PS/mysql used a separate mysql_upgrade script (built into PS 8 now?) and I remember there were hoops for upgrading with debian packages in a replicated env. We had to disable the binlog on any Masters temporarily to avoid all the upgrade statements from entering the binlog and executing on Slaves. Is that still the case? or do newer versions of PS skip the binlog for upgrade related statements?
By default, since MySQL 5.6.7, mysql_upgrade does not binlog queries - https://dev.mysql.com/doc/refman/5.7/en/mysql-upgrade.html#option_mysql_upgrade_write-binlog It’s the same in Percona Server.
Now, MySQL 8.0/PS 8.0 does not use mysql_upgrade script any longer, as system schemas are upgraded by the mysqld binary itself: MySQL :: MySQL 8.0 Reference Manual :: 4.4.5 mysql_upgrade — Check and Upgrade MySQL Tables