Everything you're saying also applies to non-tangible property rights generally, which includes property rights to land (and the accompanying rights to airspace above that land or mineral rights in the ground), and rights like:

• A first round draft pick in the 2031 NBA draft
• A noncompete agreement where your CEO agrees not to work for a competitor for 12 months after working for you
• The right to a window view of the ocean, to restrict your neighbors from building something too tall
• A ticket to enter a music festival and sit in first come, first serve seats in the grassy area
• The right to kick out a person from your restaurant that is otherwise open to the public

Each of these are enforced by some kind of adjudicatory body (which we can call a law and a state if you'd prefer). But that would be true of anything like a copyright or a trademark or the right to one's image/name.

And so we're still basically talking about how strong the right to property or the right to contract is, and what types of rules/rights will not be enforced by the courts, and which will. Some types of contract terms are unenforceable, and some property rights are limited.

Can you imagine somebody asserting rights over the cider you made with the apples he sold you?

What about someone asserting rights to the apples you grow on the land they've leased to you? Or asserting rights to the water that flows across the land they sold to you? That kind of stuff happens all the time.

The fact is, libertarian doctrine is generally in favor of a strong rights to property and contract, and that's why many libertarians are strongly in favor of strong IP rights.