I have put quotes on 'Coaching' because it's such a vague term. What exactly is meant by coaching in the context of singers or instrumentalists?
As far as I'm concerned, it simply means giving helpful advice, which can be of various kinds. Sometimes a qualifying word is added - for instance, some people describe themselves as a 'vocal coach' or 'language coach' for singers. The latter is obvious - it's someone fluent in the language who can help with pronouncing it correctly and with delivering it so that it makes sense. A vocal coach is someone with enough knowledge of singing technique to give what almost amounts to a singing lesson, though maybe with slightly less detail than a full-time singing teacher may use.
All repetiteurs give what I think of as 'note-bashing coaching' - making sure a singer is singing the right words, on the right notes, at the right time. In addition, we can often give some guidance on matters like style, breathing, possible rubato moments and so on, and many of us can give basic language coaching in some of the commoner opera languages - Italian, German, French, English, maybe Russian and Czech.
I can give help with:
Basically getting it right - including awkward contemporary scores, which are something of a speciality;
Stylistic advice from Mozart to the present day;
Detailed style and 'tips and tricks' in Wagner's operas;
Detailed language coaching in English and basic in Italian, German and French
There are few operas in the standard repertoire that I haven't had at least some contact with and my library includes over 120 opera scores. I also have a very wide knowledge of the song repertoire and the oratorio (etc.) repertoire.
As far as instrumental coaching is concerned, I have long and broad experience of chamber repertoire and can generally make at least a few helpful comments.