Re the possible change to "New in version V." text, my proposal there is the make this become:

    New in :ref:`version V <whatsnew-V>`.

by modifying the definitions in sphinxdomains/changset.py from:

versionlabels = {
    'versionadded':   _('New in version %s'),
    'versionchanged': _('Changed in version %s'),
    'deprecated':     _('Deprecated since version %s'),
}

to:

versionlabels = {
    'versionadded':   _('New in :ref:`version %s <whatsnew-%s>`'),
    'versionchanged': _('Changed in :ref:`version %s <whatsnew-%s`'),
    'deprecated':     _('Deprecated since :ref:`version %s <whatsnew-%s>`'),
}

and adding a:

    :: _whatsnew-3.7:

to Doc/whatsnew/3.7.rst and likewise for the other whatsnew files.

That requires a change to both the docs and sphinx, and is independent of the PEP reference additions. I'll make a distinct PR for this, unrelated to the other PRs.

In an ideal world we could be more precise by using one of the _whatsnew37-feature anchors where they are present, but I don't see how to integrate that into the versionadded directives (absent something quite intrusive). The above change makes a docs-wide sweep immediately without additional work.