Use bigger machines instead of more machines.

There's always a limit on how big you can go, and a smaller limit on how big you should go, but eitherway it's pretty big. I wouldn't go past dual Intel Xeon, because 4P gets crazy expensive; I haven't been involved in systems work on Epyc, 1P might be a sensible limit, but maybe 2P makes sense for some uses.

If multiple cores/threads shouldn't be considered vertical scaling, what should?

Overclocking a single-core processor from 2.8Ghz to 4.2Ghz can only take you so far after all...

Yes, because it's still a single system image (one running OS with one process table).

'Scale up' vs 'scale out' are, to me, more intuitive terms for the same thing. Up/vertical are aligned, I guess

Usually it involves having an insane amount of ram and keeping the entire DB in ram.

I have found this to be a helpful resource when it comes to scaling in general.

https://alexpareto.com/scalability/systems/2020/02/03/scalin...

Get a more powerful single machine (in contrast to multiple machines). However I wonder if multisockets Xeons count as vertical or horizontal. I never understood how programmable those machines are..