What do the empty portraits do

After you've gotten 500 power moons, you'll unlock the cleverly-named:

The Darker Side

Which, like the previous area you unlock, is super difficult. Instead of

boss refights

You will now have to do a bunch of difficult platforming.

There are two kinds of paintings in the game. One you can encounter "in the wild"; they lead to various kingdoms; the others lead you to a "sub-level", or such.

Some of the portal paintings are filled regardless of what you do; they usually let you have a peak at some kingdom you've yet to visit, or bring you to the one you've already been to.

The unfilled paintings are mostly portal paintings which you've not unlocked yet. They usually lead to kingdoms which you're not supposed to see yet, such as the one in the Cascade Kingdom; they unlock only when you've reached the other kingdom by normal means.

The moon church painting is not a portal painting, it is similar to the one right in front of it, and is the only blank painting of it's kind; it unlocks when you collect all non-shop moons, i.e. 880 of them.