Part time contracts seem to be quite rare "in the wild". However, every contract I have got through my network and personal outreach has been much more flexible and created longer-lasting relationships.
The more you look into mid/long term fulltime projects as a freelancer the less you consider yourself a real business in my opinion.
Let me know in case you are looking for contractable devs.
As a freelancer / contractor myself I wish there were more website for that, but the quality of all these project marketplaces aren't great at all.
Besides, mid/long-term projects pose some risks for the freelancer and often the company, too.