Yes. Put concisely: Use the client tools from the newest version involved for all steps.

Isn't that impractical for most Linux distros? You'd need to manually install the new client.

On Debian (and probably most of its derivatives), the package manager will not remove any running PostgreSQL versions and will let you have multiple versions side by side. It also has its own tool pg_upgradecluster, which can perform the upgrade using pg_dump+pg_restore or pg_upgrade (optionally with link or clone options).

Probably? Certainly if you rely on distro packaging for it, yes.

I was just trying to simplify the guidance here. :)