You are describing two different problems. Do you want a shapely package that runs on your system or do you want to compile shapely against the GEOS on your system. In case 1 it is up to the package maintainer to package and ship a version of GEOS that works with your OS, python version, and library version. If you look at the shapely page on pypi you'll see something like 40 packages for each version covering most popular permutations of OS, python version and architecture. If a pre-built package exists that works on your system, then uv will find and install it into your virtualenv and everything should just work. This does means you get a copy of the compiled libraries in each venv.
If you want to build shapely against your own version of GEOS, then you fall outside of what uv does. What it does in that case is download the all build tool(s) specified by shapely (setuptools and cython in this case) and then hands over control to that tool to handle the actual compiling and building of the library. It that case it is up to the creator of the library to make sure the build is correctly defined and up to you to make sure all the necessary compilers and header etc. are set up correctly.
In the first case, how does the package maintainer know which version of libc to use? It should use the one that my system uses (because I might also use other libraries that are provided by my system).
The libc version(s) to use when creating python packages is standardised and documented in a PEP, including how to name the resulting package to describe the libc version. Your local python version knows which libc version it was compiled against and reports that when trying to install a binary package. If no compatible version is found, it tries to build from source. If you are doing something 'weird' that breaks this, you can always use the --no-binary flag to force a local build from source.
If you want to build shapely against your own version of GEOS, then you fall outside of what uv does. What it does in that case is download the all build tool(s) specified by shapely (setuptools and cython in this case) and then hands over control to that tool to handle the actual compiling and building of the library. It that case it is up to the creator of the library to make sure the build is correctly defined and up to you to make sure all the necessary compilers and header etc. are set up correctly.