Use PyWeakref_GetRef and critical section in BlockValuesRefs
- [X] Related to #59057
- [X] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).

Perf impact? IIUC we'll need to wait for the next cython release based on your PR https://github.com/cython/cython/pull/6538? I've updated this PR so that it's not blocked on a Cython release. A review would be very helpful. The failing CI jobs seem to be unrelated: The pyodide one fails on main as well, and the manylinux one seems to be related to a docker fail, will probably be okay if rerun. This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Can this PR be merged? Is there something else I can do to push it forward? Thanks @lysnikolaou 