Who is at fault here? Yes, Bethesda for its pricing, but shouldn't Valve point that out for me (and the publisher)? Or is this a bug maybe? Usually buying such a multi package gives you (and me) a cheaper price than both individual products on their own, in addition to their individual special offering.

Could it be related to the EU handling fee?

Not really, because none other packages are affected. Usually a bundle has its own offering, where it adds offering on top of to the individual. An example would be how this works like in this (currently active) bundle, notice the 10%:

Yeah, this is weird. I already own the game and the package is still listed for €16,49. Normally it would say something like "complete your bundle" and list the price of the item you don't own yet as the total price, but it doesn't. So I guess this isn't listed as a bundle and that's what's causing the issue. Probably Bethesda's decision.

I think it is a bundle, but it ignores the individual prices. Usually the bundle price drop is added on top of the individual prices.

I just noticed your Skyrim screenshot says "items included in this package" instead of bundle, so a package must be different from a bundle. It's kinda scummy to me with expectations like this though.

Edit: this link has more details: https://steamcommunity.com/discussions/forum/1/2592234299566324683/

Seems like its a fixed price. Besides the "completion" where you don't pay stuff you own already in a bundle, the base discount of the bundle is added on top the individual prices. The fixed package price seem not to care anything going on, even if it ends up being more expensive. At the very least they could cap it at to the sum of individual prices.

Usually if I buy a game on its own, and Steam notices there is a bundle where you could get the game cheaper, then there will be a note on the cart page before checkout. But there is no notice for this case (on Skyrim+Anniversary) with packages. So I thought it might be a bug.

Yeah, that's what I think is scummy. You expect it to be cheaper, not more expensive. Good thing you noticed it. And thanks for your post, now I'll make sure I check the prices on those things.