Just use a stainless steel pan and a pat of butter.

There's no option to not use fat/oil if you don't want non-stick.

Cast-iron is not a great choice for eggs because it holds too much heat, so if your temperature goes too high up you can't bring it back down quick enough and your eggs will crisp/burn. And both cast-iron and carbon steel are a pain to maintain (keep seasoned and avoid rust). (Cast iron is ideal for other uses though, particularly searing meat, where holding heat is the main feature.)

Also, the idea that a cast-iron (or carbon steel) patina is somehow non-stick is a myth that keeps getting repeated. It's better than the raw metal (and therefore quite necessary for those materials) but it's nothing like an actual non-stick pan. Nowhere even close. And you still always need a normal amount of oil for cooking in them, in fact just for maintaining the patina.