We need to make a difference between users who are 100% away from the wiki, and the ones who remain around, but who don't have enough time to help newcomers. so we need to have two away systems: one for the wiki, and one for mentorship.

In T329052#8593784, @Trizek-WMF wrote:

We need to make a difference between users who are 100% away from the wiki, and the ones who remain around, but who don't have enough time to help newcomers. so we need to have two away systems: one for the wiki, and one for mentorship.

Good point. But mentors might want to use the generalized one, so that they could use the auto-responder or modified user signature appearance. If we do this work, we'd need to think about how to set this up so it works in a coherent way for mentors/mentees.

optionally (up to the user to enable) modify the appearance of the user signature so that it's obvious that they are away

That would only affect new signatures, since after saving the comment the signature becomes a normal part of wikitext. I think it would cause way more confusion that benefit.
(One thing that would be done is to make Linker/LinkRenderer add some kind of styling to the user page / talk page, e.g. a different color. Doing that in a performant way might be nontrivial, but possible, e.g. via the GetLinkColours hook.)