Hi and Welcome
Good info from Christie. I switched to no dig a large number of years ago. One of my issues after doing such was leaving the soil bare. Naked soil! As you said you have access to a lot of leaves, I'd recommend getting some leaves, shredding them, a lawnmower will work, and putting an inch or so of leaves on top of the soil. Maybe let your compost keep aging and apply it to the beds at the end of the season would be the best use for it. Saying that... I have used unfinished compost as a mulch around plants and it works well.
As far as the carrots, what I think I'd do is put the shredded leaves close to the carrots but not on top of them and as the carrots grow gradually push the shredded leaves around the carrots.
I tried an experiment a couple years ago. I places a three inch layer of leaves on top of each raised bed, hoping they would decompose and attract beneficials by spring. Three inch layer was just toooo much. The top inch or so was starting to break down but everything under it was dry. I don't remember if we had a lot of precipitation that winter or not. Didn't have time last year to try again, but best thing in my opinion with the no dig, is to add compost at the end of the season and letting the soil organisms enjoy it and transport it through the soil column throughout the late fall and winter.
The charcoal and ash... I add those to the compost. You could add the charcoal directly to the bed, and I did when I took the ash the compost pile and saw a large chunk of the charcoal in it. I break it up with my hands. The ash.. I just add it to the compost. Takes away all the worry about pH levels when applying the ash directly to the bed/plants.
Grass clippings will work, I'd let them dry out for a couple days before applying. To dry out the clippings, spread them out in a thin layer. If you don't the grass clippings will clump, might go anaerobic on you, and could burn your plants. Also apply the dry clippings in a thin layer so water doesn't run off.
Lasagna beds are the coolest! If you don't need one of those empty beds this season, I'd encourage you to build one to experience it for yourself.
Sounds like you're already a believer in not disturbing the soil structure going forward.