I actually cook all my veggies for the week all at once and then save them in the fridge, so they're all pre-cooked before I add them to the skillet. Saves a lot of the fiddly trial-and-error checking to see if my carrots are done at the same time as my broccoli or whatever.

Except onions, garlic, and chili flakes. Those get cooked in the oil before I add all the other veggies.

Garlic and onions first, mushrooms next (salt them so they release their liquids and brown), carrots/sweet potato/potato/beets/ any other very dense veggies next, then broccoli/Brussels sprouts and cauliflower types of brassicas, then cabbage/kale/chard, then lighter leafy greens. With things like spinach and arugula I pretty much turn off the heat and fold them in whatever I'm making immediately and toss and they'll cook down. It is also debated whether garlic should be added early or not, you can kinda do with it what you will.

A lot of this comes down to trial and error in terms of how long to cook things before adding the next. Use a fork to poke, and use your teeth to bite. Say if I'm cooking broccoli, I'll give it 5 minutes then eat a small piece to see if I like the texture. Hard as a rock still? Another few minutes, poke with a fork, if its softer but still tough, ill add the next "layer" of veg. If I'm just adding leafy greens I'll let things like sweet potato/carrot/brocc cook all the way through then add those and cook for 1-2 minutes.

As a rule, cook time is related to size and density. The bigger the longer it takes and the denser the longer.

As a general rule of thumb harder veggies have more fiber and need more time to break down, but in my experience it's really all about how small and into which shapes you cut your stuff. Also kinda depends on what you wanna do really, if you're trying to get color on stuff don't overcrowd your pan, but if you just sorta wanna sauté/steam your stuff, you can add more stuff at once and sorta layer it while keeping it moving.