They typically coat your nasal passage in with stuff that makes it hard for virus/allergens to survive. Betadine has something called iota-carageenen, which comes from seaweed, and it envelops small particles like a virus before it interact with your nasal passage and infect you. Other sprays have different formulas and do slightly different things, but essentially attempt the same type of thing. Betadine helps my allergies so in my experience I can tell it's intercepting allergens at the very least.

Not foolproof, and not a good sub for masks, but it helps your odds a bit.

And one of the ways covid can enter your brain is through the olfactory bulb in your nose, which is why so many people have long term problems with smell, so protecting that is probably a good idea.