> We (ideally) change our beliefs with every new piece of input. That's good.

sounds like a cope. like shifting goalposts. or no true scotsman fallacy.

if I see a tree in front of me, and 2 seconds later I close my eyes, and someone asks me if there is a tree in front of me, should I say yes because I "know" it, or because I "believe" it ?

In that 2 seconds, the tree could have fallen down. So if i said "yes", I wouldn't be lying but I would be incorrect.

Therefore all "knowledge" is belief about some past "truth". Whether you call it faith, evidence-based, dogma etc. they all do fall under the same bucket if you think deeply about it.