Since quarantine life, I've been cooking multiple times a day. My oven's self-clean makes my pans look exactly like new. Takes all of the black off leaving them with a shiny, silvery shine. I then have to season them to regain a nonstick coating as good as any Ceramic/Teflon pan that I've used.

As far soap. My experience is that it definitely damages the nonstick coating, depending on how much you use. You can get by with a soapy sponge, but putting detergent directly on it and the nonstick coating will be lost.

The best way to avoid need to avoid soap or scrubbing and re-seasoning is to put hot water in the pan while it's still hot and scrape. Meat is the worst for leaving a coating and this technique removes 99% of it.(If not blackened use that water for a delicious sauce with all the best flavors of your cooking). This routine allows me to use the same pan for months without a deep cleaning.

I have tried to put cold oil on after heaving soaping, but I'm not happy with the pan until I season it with high heat. The only reason I'd do it for rust and still would pan on seasoning it properly later.