I think we should be careful about the word property. In the case of copyrighted works, you do not own the work, you own the copyright to it. In the same way with patents, you don't own the patented idea, you own the patent. Both of these are abstract constructs that means society gives you certain rights, but do not extend ownership to the ideas. This is plainly obvious with regards to copyright since the fair use clause gives anyone right to make copies under certain circumstances.
Even in the case of land ownership, one could argue that what you own is much closer to a "license to use the land surface" since you can have surface rights without having the rights to mine or drill for oil on that land.
So your idea that property comes about because government says "what else is valuable for people that we can protect for them?" I think is incorrect. Property rights aren't some God-given right, we as citizens agree to handing out the rights to pieces of the commons to individuals because there is some net gain to everyone from this. All of those "rights" you describe are therefore subject to an evaluation of whether they serve society's purpose, and I think it's pretty clear that's a discussion that is very relevant to patents and copyrights.
I agree with everything you just wrote, so if I came off as contradictory it means I wasn't clear about something. When said "government says," obviously it was a bit of hyperbole, I really meant that citizens and government agree on a set of rights, pursuant to certain goals we have as a society, and how they should be distributed. Of course there are subtleties that I tried to gloss over, such as owning a patent vs. owning an idea---I was just trying to emphasize the fact that even ownership of material property is such a right, based on agreement, and is basically already an abstract concept, and therefore consistent with other forms of ownership that may seem more abstract.
Even in the case of land ownership, one could argue that what you own is much closer to a "license to use the land surface" since you can have surface rights without having the rights to mine or drill for oil on that land.
So your idea that property comes about because government says "what else is valuable for people that we can protect for them?" I think is incorrect. Property rights aren't some God-given right, we as citizens agree to handing out the rights to pieces of the commons to individuals because there is some net gain to everyone from this. All of those "rights" you describe are therefore subject to an evaluation of whether they serve society's purpose, and I think it's pretty clear that's a discussion that is very relevant to patents and copyrights.