As someone who was contracting we always had notice periods in contracts. Let’s not forget it works both ways and contractors are more often than not the first to go.
Sounds more like a temporary employee than a contractor then. Maybe splitting hairs.
When I was freelancing, I would have a Master Service Agreement that spelled out the "rules of engagement" and the actual work was in a Statement Of Work that lasted roughly 3 months. Gave each party the ability to pull the rip cord