The interesting thing is that, at least for my tests with arrows, the Owner ID stays with the arrow even after it goes through the portal. All the NBT data stays, but because the Owner ID can only be connected to a player in the same dimension, it isn't able to find that player and apply specific effects to whatever is getting shot.
I was wondering if you could somehow introduce the UUID of the Owner in the same dimension by summoning in that player's player head, but no dice.
Hi, I've attached a demonstration video and a world download that I used for the demonstration