Backport PR #59136 on branch 2.2.x (Upload 3.13 & free-threaded nightly wheels)
Backports of:

- https://github.com/pandas-dev/pandas/pull/59208
- https://github.com/pandas-dev/pandas/pull/59136
- https://github.com/pandas-dev/pandas/pull/59401
- https://github.com/pandas-dev/pandas/pull/59819

which together should enable Python 3.13 wheels
Should probably directly include https://github.com/pandas-dev/pandas/pull/59819 as well, once that is merged wait for #59837 Thanks Joris!