Someone asked a question about what you would change from the movie and one of them was to give Rapunzel a crossbow. Was Rapunzel supposed to get a crossbow? Some of the toy merch for the series had a floral bow and arrow set that NEVER appeared in the show either. Was Rapunzel learning archery a scrapped concept?
Oh, my darling, my love. I will be glad to show you.
Rapunzel with a crossbow comes from the pre-Eugene version of the movie. The one being directed by Glen Keane, with Bastion as the male lead.
Art by Dan Cooper
Art by Dan Cooper
Art by Jin Kim
So, yes, there was a point in this movie's production where Rapunzel defended the tower with a crossbow rather than a frying pan.
And then, as you mention, there's merch from the series of a carved and painted bow.
Art by Heather Chavez
The thing is, there is so much very specific detail on this - like the deer and bird on the quiver, that it’s difficult for me to think that this design did not come from the series production team. While I have no confirmation of this, I highly suspect they wanted her to have a bow of her own, and Disney told them no. I do know that they were only allowed to have her hold a sword in the series if she wasn't actively using it against a person at the time. (Yes, she could be holding it with intent to use, but not actually be seen swinging it on camera at a person. I have a gifset showcasing all the times she held a sword.) So it's not a far stretch to think that they intended to give her a bow, even had a toy designed for it, then were ultimately denied by the higher ups. But toys often get put into production before things get changed in the media the toy represents, and then released anyway.
