I really don’t think it gets much easier than just cracking eggs into a pan personally, if you’re finding your having a lot of trouble with cooked-on egg gunk, that sounds to me like a technique/skill issue, pan to hot or not letting it preheat enough and/or not enough oil/butter/grease.

Get those variables right and you shouldn’t really have much cleaning to do, I can pretty much just rinse and wipe off my pans after frying an egg, no real scrubbing or scraping or anything needed no matter if I’m using stainless, nonstick, cast iron, etc.

If hard/soft boiled eggs are appealing to you, I have a little dash egg steamer doohickey that works really well, although personally I think peeling eggs is more fiddly than cleaning a pan

There’s a few doodads out there for poaching eggs in the microwave, but personally I’ve never had much luck with them, they always seem to come out overdone or explode which makes for more cleanup than a pan.

There’s a few ways to do eggs in the oven, my wife meal preps egg whites with various mix-ins in some oven safe glass containers and just heats them back up in the microwave throughout the week.