I'd like to be able to manually order/prioritize my wishlist, but I don't see a way to do that. Is that not currently a feature? If not, do we know if it is planned?

That was possible in the past (more than a year ago?), but no longer at the moment. Don't know if it's planed, but GOG says there's a new version for the site in works. Coming Soon™.

Edit:
My bad, I thought you're talking about your owned games list, not the wishlist. Wasn't possible, as far as I know.

Edit2:
The only way now is to remove the games and re-add them in the order you want.

You can only sort it automatically (by name, date added and "user reviews", whstever that means), and also filter the games (by price, genre, features...).

I don't know if anyone from GOG has talked about this or other possible features, but your suggestion has already been proposed in the community wishlist:

https://www.gog.com/wishlist/site/ability_to_manually_rearrange_personal_wishlist

That's unfortunate. I'll go upvote the community wishlist entry. Is the community wishlist actually read and respected by the GOG devs?

Once in a while they mark some of the items as "in progress" or "completed". But a popular wish is by no means a guarantee that it will be fulfilled. Especially considering there is a lot of work to do on the website already (like the notification system).

Source?