A bit of nomenclature rethinking.
You could get an adapter with or w/o a carbon fork that would let you use a modern stem, I don't like the term threadless as all (almost) stems don't thread into the fork.
One way would be a 1" thread less steerer fork. Not easy to locate bur they do exist. You will then need a 1" threadless headset, those exist but are becoming scarce. Then use a 1" clamp both ends stem, aka threadless, but those are not common with 31.8 bar clamp.
Quite a bit to spend, unless you love the bike.

I would get a "quill" to 1.125" adapter and go that route. Keep the steel fork.