Work like this is more commonly described as freelance, consulting, or contracting.
If a job is advertised as "part-time" they're usually expecting you to work every single one of those hours, unlike a retainer where you're expected to be available for up to that many hours.
It may sound pedantic but it's important to understand the difference when searching for roles. If you take a "part-time" job they're generally going to want you to be working for every one of those hours, even if you have to find your own work to do. If you treat it like a retainer job where you're only expected to be on-call if they need you, you could run into some disappointment.
Using the right terms will also help you find roles that more correctly match your expectations.
True part-time work is hard to find because most companies would rather hire someone to work 4 x 40 hour weeks on a project instead over the part timer who wants to do it in 8 x 20 hour weeks or 16 x 10 hour weeks.
This leaves work that is sporadic and spread out, or companies that have a need but can't fit full-time compensation into the budget right now. That's a hint for the type of work and companies you'll need to seek out. Trying to pitch yourself as a valuable contractor who needs 3-4X longer to finish a project due to your short workweek isn't a winning strategy for most jobs.