Task: Refactor two-phase launch implementation #12574

Remark: In my attempted refactorings of this PR, I always found it better if I did not unpack or detect any stream outside in the launch function, but really just forward to environment as is, and only at the very last try to see if it responds to cuda::get_stream and potentially rewrap it with an override stream.

It seems the version here probably works as well, but we should refactor this in a follow-up.

Originally posted by @bernhardmgruber in #12379 (comment)