FWIW some of these also apply to MySQL, like the use of FKs and major version upgrades. I think scaling any centralized and business-critical resource is hard.
I assume you mean built-in sharding across multiple nodes/instances/servers? No, there's no built-in support for that in MySQL, at least when using a general-purpose storage engine like InnoDB. (There are alternative engines like MySQL Cluster / NDB, as well as Spider in MariaDB, but these are not widely used and have some major shortcomings.)
Or if you just mean partitioning across the same node ("partitioned tables"), then yes, MySQL has had that feature for over 16 years.
That all said, I agree 100% with your overall point: scaling any relational database is challenging, and I don't see any evidence that Postgres is harder than others. In my direct experience, nearly every item in the original post has some analog in MySQL that can become problematic at scale. So I'm not sure what Postgres-specific concerns GP is referring to.