Hello.

Anyone ever heard of power steering pump causing veering to one side while driving?
I've had this kind of problems since I fitted new tires. First I thought it would be the new tires, and swapped front wheels. No change....
Today I noticed when started the engine, with manual in neutral, both feet off all pedals and hands off the steering wheel, the steering wheel yanked to the right when engine fired up.
Not much, maybe 5° or so. Is this making any sense?

When was the last time you had a front end inspection and alignment?

Last month. Right after fitting the new tires. Everything was ok.

If it is doing it while driving that'* not good, and I would look at the steering rack as then being suspicious.

Sounds like the spool valve is hanging up a little. Might want to try flushing the power steering fluid. Whatever it is might come out or might not.