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Playing on our minecraft server my friend noticed a skeleton holding a golden sword, we reached a conclusion that the skeleton spawned either with no bow, or with a bow that has a durability of 0. The picture above is a screenshot I took of the skeleton (that sadly didn't survive).
I realized it wasn't an end case bug with our specific server when I saw the same thing happen to youtuber GoodTimesWithScar on his latest video (at 16:05) where the skeleton picked up their iron sword after they died.
Your conclusion is incorrect. Some undead mobs have a chance to spawn with the ability to pick up items from the ground. When it comes to skeletons, they are willing to swap their bow to a sword from the ground. This skeleton just picked up a sword that was probably dropped by a zombie piglin, this is a normal game behaviour. Also durability does not apply to mobs (except for crossbows)