All the new leaves are dying?? Idk what’s happening, it’s not in direct sunlight but it has morning sun

Should I move it to make sure?

I'd put it in bright, indirect Sun (bright light) for now. I don't know why the new leaves are turning black. What soil is it in? Very strange....

Peat and spaghnum moss it looks like, I bought it from a store so I don’t really know, maybe the distilled water is taking the nutrients? Should I repot it?

No, distilled water is fine. Not sure if re-potting would help. Maybe someone else can chime in.

Ok I’ll repot it in a bigger pot since it might not have room for the roots cause it is a small pot.

The root ball is actually pretty small, so it is not necessarily the pot. However, it could be the potting medium. The nursery does not necessarily use premium potting mix for the plants that they are going to sell. They want the plants to die so that you have to buy more. That is why I usually swap out or replant any new plants into its new home for the season, as soon as I can. That includes any special or better potting mix that I might think will benefit the plant better.

Other that that, maybe your morning light is still too much light. Have you moved it to be indirect bright light?

Yes

That is a extremely hardy N. x ventrata! Tough as nails with regards to Nepenthes. It really looks like those are some type of burns caused by hard water or something getting on the plant, maybe before you got it. Fertilizer burns, pesticides, hard to say. I have absolutely no problem using tap water on these plants and save the expensive distilled water for other plants.

Give it time actually it looks decent with new growth and good color. the potting medium looks problematic so fresh repot will help. It will also set the plant back as it acclimates.

If that peat has dried it is useless to rewet and that medium doesn't look moist enough, .