CLN: fix and move using_copy_on_write() helper out of internals
I initially added this helper function just to the BlockManager internals in https://github.com/pandas-dev/pandas/pull/49771, but since then it seems we also started to use it outside of the internals. Which I think is a good change for a check that we will have to do often on the short term (it makes it more convenient to do this check, see the improvement in the diff where I changed existing `get_option(..)` calls). 
But, 1) the current function was only meant for internal usage and was incorrect for usage outside of the BlockManager (it also needs to check for the manager option) -> fixed that, and 2) moved it outside of the internals, so we don't have to import it from the internals in other parts of pandas.
> Should we merge this now? Would have to adjust all our PRs afterwards.

If that's OK for you, I would maybe merge this first? 
(we could also first merge the other PRs, and then update this one before merging. But since we will probably keep opening other PRs related to this, we will just need to merge this at some point anyway) Yeah lets do it now thx @jorisvandenbossche 