I have a 2011 Mazda3 and the power steering fluid reservoir is nearly empty. I was hoping to buy a bottle of something and just pour it into the reservoir. The user manual says to use "Mazda Genuine ATF M-III, M-V, or equivalent (e.g. Dexron II)", but I am confused because I don't know how to choose, nor do I know how to determine which of the products I could buy at Advance would be compatible, nor do I know if it's important to make sure I put in only the same exact kind of fluid that's already in there.
Looking for advice on what to buy and whether me topping it off is a good idea. Also generally curious what a mechanic would do if I took it to a shop (would they do a fluid exchange or just top it off, and in either case, what would they likely put in).
Update: I'm looking for an answer based on first principles and foundational knowledge, with reasons.