Unable to start a DLC, when it's installed at a further date - compared to the base game

I first noticed this with Beat Saber.
I had the game for a long time, then i installed the newest DLCs - but they were nowhere to be found in the game.

Then I just noticed it again with Cuphead.
I had beaten the base game, but the DLC was not installed.
Now I installed the DLC, but it is not available inside the game.
I made sure that it's the right version - the right region.

In the notifications, where it says that the DLC is installed, when i press X (on the DLC notification), it opens the Cuphead game, where my save is recognized.
Therefore, the DLC is for sure the same region as the base game.

But I can't understand why the DLC is not recognized. This game makes it two out two.
Both Cuphead and Beat Saber.