Are there any ingredients I should not add to a no-knead dough with an extended proofing time?

I don't think there's anything specific to worry about with bread dough. The important point is the temperature: if you're considering adding an ingredient that you normally wouldn't let sit out at room temperature for 18 hours for food safety reasons (and/or because it might start tasting "off"), you probably should add that ingredient toward the end by folding it in before shaping or something.

Most no-knead bread recipes that sit out at room temperature for a long time are quite flexible. You likely won't cause any problems by folding in an ingredient late in the first rise.

I’m no expert but I’ve seen this discussed on The Great British Baking Show. They recommend adding things after the dough rises, when shaping the loaf. You could use the envelope fold method. I know it’s not strictly no-knead, but maybe close enough. One baking site thinks folding the dough a couple times improves the bread, regardless of additions. HTH!