DOC: Fix version switcher in old docs
- [X] xref #48285

Fixing the version switcher in old versions of the documentation.

I'm also removing here the duplicated 1.4 link in the version switcher.

I'm adding here `1.5` to the version switcher dropdown. Docs for 1.5 are already published, I just need to change the link to the stable docs once the pypi and conda-forge packages are published. But I guess we can merge this even before, since the dropdown is currently broken, and this should make everything work, except for the 1.5 option that will go to the 1.4 for few more hours. @phofl do you mind having a quick look at this please? Thx @datapythonista 

1.6 is fine as milestone? > 1.6 is fine as milestone?

I think for PRs only affecting the website we don't need to backport anything. Is the milestone useful for anything else other than backporting?

Looks like this PR didn't work as expected. :( Luckily I understand the problem now.

In the new version, the `url` in the json is being used, but in the old versions, it's the `version` field which is relevant. I think we set up things incorrectly at the beginning, that `version` field had to be something like `1.4.4`, and use the `url_template` to provide how to build the whole url with it. But instead, we used `pandas-docs/version/1.4.4` as the `version`: https://github.com/pandas-dev/pandas/pull/45370/files

I can restore the `pandas-docs/version/1.4.4` values in the JSON, and the switcher will work again, except that `version` is used to match to the current version and know in which version of the docs we're in (not quite sure this works). I'll do that for now, and we can discuss later if we want to have the correct `version` values from now on, which can be done if we add a new correct json file for the new versions of the docs, and we keep the old one until the broken versions of the docs are removed from the switcher.

Funny enough, this change in behavior made that even the switcher in the pydata theme page is broken. Try to change the version in their old docs: https://pydata-sphinx-theme.readthedocs.io/en/v0.8.0/user_guide/configuring.html