I’d just aim for a full time gig and then back away to part time. I work with someone at Google who has a formal arrangement to work part time (Tuesday-Thursday).

I’m not sure their story so you may or may not scare away the recruiter if you ask for part time up front.

I’d also do the same for remote work. I have successfully converted to remote twice when they technically don’t allow full remote. Had to put the time in for that though