I tried to give an enchanted bow to a skeleton in 1.21.1 and he does not pick it up. Either thrown on the floor or equiped with dispenser. They however pick up swords without issues.

In versions 1.20 and below and he does pick it up.

Tried on a server aswell and the bug seems to be there also.

To repreduce :

Throw diamond armor in a hole,

Spawn skeletons using a spawner (for patient people) or an egg until one equips armor,

Throw a bow enchanted with flame (to confirm he equiped it) in the hole,

Go in survival to see if flaming arrows fly towards you.