actually, the moon gains angular momentum from the tidal movement that it causes, and that’s what makes it move further away. the reason is that it takes Earth about 1 day to rotate once around its axis, but it takes the moon 28 days to rotate once around Earth’s axis. so Earth has a higher angular velocity, and the tidal movement tries to reduce that difference to make the two tidally locked eventually. ironically, this process transfers angular momentum to the moon (to speed it up), which makes it move further away and thus the angular velocity actually decreases. yeah, orbital mechanics is weird.

(btw this is not a joke. it’s really that way, difficult to comprehend i know).