As a pip maintainer I don't think that's really true. The resolver in both pip and uv are fundamentally sequential and single threaded, you can't really queue up or split out jobs.
What uv does is parallelize the final download of packages after resolution, and batch pre-fetch metadata during resolution. I don't think these benefit from async, due to their batch nature classic multi-threaded download pools are probably the better solution, but I could be wrong!
Experiments have been done on the former in pip and didn't find much/any improvement in CPython, this may change in free threaded CPython. For the latter we currently don't have the information from the resolver to extract a range of possible metadata versions we could pre-range, I am working on this but it requires new APIs in packaging (the Python library) and changes to the resolver, and again we will need to benchmark to see if adding pre-fetching actually improves things.