You lot are weird.
Without milk it’s a fried egg you broke. You might want that but it’s not scrambled eggs.
If it’s not runny it’s not scrambled egg, it’s an omelette, runny means some of the egg should be runny not the liquid crap you get from too much milk or over cooking, none should be firm enough to to hold together when touched. If it’s cooked more than that it’s an omelette.
The only things beyond egg and milk allowed are salt and pepper. Oil etc in the eggs are needed because you’re over cooking them, it’s how you stop breakfast buffet eggs turning into a rubbery a solid mass in 2 minutes under lamps, (oil/butter the pan as you see fit). Salmon cheese etc *in* the eggs means you’re making an omelette not scrambled eggs.
Tip onto receptacle, season with your choice of diced chilli, balsamic, maybe some shavings of parmesan, hp sauce, smoked salmon, goat testicle or what ever. So long as its not tomato ketchup.
That being said, personally never ‘mix’ it in the pan, mix, add to hot pan and cook stir with a spatula to stop it catching but don’t set about deliberately breaking it up. I go for plonking it on of wilted spinach or chard, then top with chilli and shallots fried with a little whole grain mustard, mushrooms and garlic.