The vast majority of modern American toll roads are. I grew up in Austin. We have the Mopac and 183 expansions, route 130 was mostly privately constructed, but is under TxDOT.
Perhaps other parts of the world have privately operated roads, but I’m not aware of them.
The part of route 130 you are referring to is technically owned by texas, but under a long term lease/manage situation, I believe the lease is 50 years. It's private in practice. There are many more such situations in the US than folks realize. Chicago Skyway, Indiana toll road and others. Cities/states will contort structures to be able to say "we still own it!" while economically not owning it.
So, the ones in states that can't afford to build or maintain them are often private roads or PPP.
Australia is one of the top toll roading countries. Sydney had most tolled roads world record for awhile not sure who holds it now. I don’t know whether it is the state or private companies who operate them.
Since you live in the area, and are talking about toll roads, I assume you also probably know of the name Cintra, who are Spainiards. And Cintra is, in fact, a private toll road operator who has owned roads around Austin previously
My point here is that a privately operated toll road that exists purely as a toll road, does not parallel the concept of a moderately expensive subscription for what is effectively an existing product. A more apt comparison would be a toll lane in an existing road, first class compartments, etc.
Perhaps other parts of the world have privately operated roads, but I’m not aware of them.