In Australia it's customary to thank the staff members attending your table. So when they top up your water, or lay out cutlery for the next course, or clear plates, you say 'thanks/thank you'. Same for people clearing glasses in bars. It's like a millisecond pause in your conversation to thank the staff member; it's basically cell memory, you don't think about it. They may or may not acknowledge it with a smile or 'you're welcome/no worries'. . It's just a basic manners thing.

I and my partner were doing it in the states and it was clearly unnerving the staff. Lots of puzzled looks or 'thats ok hun' like they had to reassure me that it was part of the service.

Do people just ignore staff there? Is paying a tip at the end the only acknowledgment that they exist?

Once I knocked over some products in a store and then picked them up. The staff acted like that was saintly, so I guess other people just make a mess and move on?

sometimes it happens. Depends on the person and where you are sometimes.

Generally if someone accidentally knocks something over they'll put it back, though it's not uncommon that stuff gets put back in the wrong place, i'd say that's more common.