In this world with renaissance-like technology wizards are able to "feels" creases in the 3D space and manipulate space in ways limited to their understanding of the 4D (wich is still not fully understood). They are able to do wormhole transportation but the two ends of the wormhole are fixed to a specific geographical point and teleporting living things usually kills them. Some plants also use this creases in space to teleport sap to the canopy so they are able to grow larger. Opening one of this wormholes is difficult and takes time but perhaps other interactions with the 4th dimension are more easily done. Besides teleportation and what I mentioned, what other kinds of things would be possible?
A 4D creature interacting with 3D creatures could do about as much as we could do if we were to intersct with 2D beings.
Now there may be some that say that we need at least three spatial dimensions for life. But handwave that away and imagine we had a world of animated stick people on a sheet of paper. Also we are able to cross that sheet without damaging it.
The stick people only see our 2D projection in the sheet. Also, no matter how much we twist the sheet, it seems flat to them.
So we can twist the sheet to connect ends and make infinite loops of their space, and connect distant points. You already imagined something like that when you said wormholes.
What else could we do? From outside the sheet, we can see the inside of any enclosed space they have. Like a box, or a house with all its doors closed... stick figures inside it cannot see those outside and vice versa. But we 3D creatures can see through everything that is in the sheet. We can also appear and disappeae from inside their closed spaces as if we were ghosts since we can cross the sheet from any point, so we could take a 2D diamond from the inside of a 2D safe without ever having to open that safe. No wormholing involved... though if we then place that diamond back in the sheet anywhere else it will seem like teleportation to the stick people, even though it isn't.
Last but not least, we could take an object out of the sheet, flip it horizontally, and place it back. For the stick people, it will seem like the object became the mirror image of itself. In 3D terms: someone might be pulled out of this 3D world, and if flipped and put back here, their insides are flipped. Suddenly someone who was left handed and had a tattoo on the left arm is now right handed and the tattoo is on their right arm. The person's heart would also be more on the right side of their chest. The liver and spleen would seem like they switched places.