look, onion tops are taller than carrots, and they don't shade things
very well. if anything, you need to worry about the onions shading the
carrots.
second, the carrots are also fairly shade tolerant, so why not deploy
the carrots elsewhere, like at the base of tomatoes. finally, onions
like nitrogen, but carrots hate it, so no way you can get both large
onions and smooth carrots. Companionship or not, you never interplant
crops with very different nutrient requirements.

I usually plant lettuce amongst the onions, with the lettuce holding up
longer than normal, up to mid-july, because of the partial shading by
the onions. The lettuce keeps weeds down (always a problem with onions
or garlic).This year I might interplant beets instead. when the onions
go in mid-august, I plant bokchoi seedlings in there right away. All
three crops like wood ash and nitrogen, and of course the soil is very
rich in organic matter.