Switching to mw.cookie would mean that cookie name would/could change (to be prefixed according to wiki config, e.g. with the wiki name) - it could actually be a reasonable change.
If the name of the cookie changed, there should either be backwards-compatibility code for a needed period of time (if possible), or the cookie would be required to be set again (i.e. e.g. user will be presented again with the popup and will need to close to set the new cookie).

Problem here only apply to the experience of non-logged in users.

Cookies involved are related to the following things:

• "term box" initially collapsed/expanded
• showing the copyright notice on edit
• showing the IP notice on edit

See also discussion in https://gerrit.wikimedia.org/r/#/c/388459