Despite his arms having fallen off, this is St. Peter as apparently he can be identified by his hair. I’d add that I wouldn’t have known that, this is the view of the museum and I have no reason to doubt them.
The museum notes that this was made in the city and was inspired by the Cologne Cathedral sculptors and perhaps this is also from the same building. It dates from between 1315 and 1320 and is made from walnut.
He looks like a cheery soul and this polychrome sculpture is in quite a solid state of repair given its age. It’s a shame that more isn’t known about its provenance and what churches it has likely spent most of its time in, but I doubt that it has been out of Cologne for very long.
And back to AI to show what it might have looked like.