I have not ran MySQL for some years but it at least used to have exactly the same issue. Upgrading a database with MySQL can take a long time if you have many tables. The main difference is only really that PostgreSQL does it with a separate tool, pg_upgrade, while MySQL does it as part of the main binary.
For both MySQL and PostgreSQL you will need to use some kind of logical upgrades if you want no downtime.
They don't change the on-disk structure all the time though...
Mostly because MySQL development is slower.
MySQL has advocated for decades spinning up a replica with the upgraded version, waiting for it to catch up to master before promoting it to the new master. You can do the same thing with Postgres.
Exactly, MySQL and PostgreSQL are the same here. Maybe one is a bit faster than the other at doing major version upgrades but the behaviours are quite similar.