DEPR: remove Index._is backward_compat_public_numeric_index
Removes the attribute  `Index._is backward_compat_public_numeric_index`and related stuff. This is the last PR before actually removing Int64/UInt64/Float64Index from the code base.

This PR builds on top of #49560 (which is not yet merged), so please exclude the first commit  from review of this PR.

I'd also truly appreciate if someone could review #49560, as it's quite a heavy PR with lots of dtype changes.
Could someone take a review? E.g. @jbrockmendel or @mroeschke?

I've rebased this after #49560 has been merged.

After #49560 and this will have been merged, the removal of Int/Uint/Float64Index should become quite straight forward. 
 Thanks @topper-123 