That's the point. We don't do that. You link to the system libcurl dynamically and everyone is told to do the same.
If you want to use a private curl as an implementation detail then the only safe way to do it is to ship a .so, make sure all the symbols are private and that symbol interposition is switched off.
If you ship a .a then the final link can always make symbols public again.
There's also a sort-of informal "standard library" of C libraries that have super-stable ABI's that we can generally assume are either present on the system or easy to install. Zlib is another one that comes immediately to mind, but there are others as well.
If you want to use a private curl as an implementation detail then the only safe way to do it is to ship a .so, make sure all the symbols are private and that symbol interposition is switched off.
If you ship a .a then the final link can always make symbols public again.