[...]whether jump should just consume movement speed. I think I’ve seen folk say that the latter is per 5e?
That's correct - Jumping is just considered a part of normal movement in 5e, and there are some simple rules to govern how far individual characters can jump without risk or stress; attempting to jump further is recommended to call for a check (athletics), and there are some guidelines for how far one could reasonably extend their jumping in this manner. The main rule outside that is that you consume one foot of movement for every foot you jump, and you cannot jump more than your movement allows (i.e. that is simply consumes your movement directly).
