Thank you @DMehaffy for your help!
I ended up going for a slightly easier solution with a Galera cluster of MySQL databases without ProxySQL and HAProxy layers.
One thing I quickly understood is that even though I make changes in the db cluster through one Strapi, the other Strapis will only see updates from existing tables but not new tables (I mean Collection Types). I guess I have to copy the code that was generated by the first Strapi into the other so it would know how to read that data from the database.