Depends on the area, but the vast majority are owner operated.

The question begs some other questions though.

One is more about what fraction of the economic production of the farm industry is owner operated; There is a long tail of now-tiny farms that are not economical to actually sow and harvest, which nobody could actually earn a living from. If it's 10 acres and somebody bales hay at almost breakeven, is it really a farm?

Conversely, there are a lot of very productive 5000+ acre farms comprised of many older properties combined together that are "owner operated" in one sense, but demand many farmhands and a lot of machinery to manage.

The vertically related industries have also seen a lot of consolidation. There are ~four seed companies, only a few pesticide companies, two main tractor companies, only a few slaughterhouse companies, etc. There are long-term contractual arrangements with some of these entities. Is an owner-operator farmer who controls so little of the business directly they may as well be a sharecropper really counted as a farm?

>Don't most farmers own their own farms? (or work on a corporate monstrosity farm).

Why not both: https://en.wikipedia.org/wiki/Cargill