Already notified insurance about a at fault accident. Is there any point settling after that?

I bumped into somebody's car in a car park and left a note. by the time they had called me they had already informed their insurance company Unfortunately. they asked for my insurance details which I provided but then said they would be willing to settle after I asked if they could get some quotes.

If I was to pay I would of course get in writing that this is to settle the claim in full but I informed my insurance company as it seemed likely it could result in a claim if the quote is too high and as they already have my details. this now will impact my premiums for the next 5 years seemingly regardless if we proceed with a claim or If I pay out pocket.

As there was no damage to my car, my excess won't apply so the insurance company will pay whatever the claim is. My no claims discount is protected so it won't be affected from this claim but I'm wondering is there anything else I'm missing because it seems cut and dry that I should just let the insurance deal with it as my premiums have already been affected. I'd only be protecting my no claims if I was to have another accident.

I'm planning on changing provider for my insurance next year and I'm wondering will the no claims protection reset giving me one claim before it starts to reduce? As my current provider reduces the discount with protection if you make two claims within 3 years, so wondering if changing provider would let me reset my no claims protection.

Not seeing many reasons to not go through of insurance at this stage but looking to seek advice as I should have done before informing my insurance company. It seems as it could very well be settled and forgotten about had I not done that.