Use common routines for `pip install` and `pip sync` (#3737)
## Summary
This PR takes the functions used in `pip install`, moves them into a
common module, and then replaces all the `pip sync` logic with calls
into those functions. The net effect is that `pip install` and `pip
sync` share far more code and demonstrate much more consistent behavior.
Closes https://github.com/astral-sh/uv/issues/3555.
