I only address breathing if I can tell the client is doing something that needs to be corrected. Natural breathing can be slightly different for everyone, but it is usually adequate for most exercise programming. You should intervene if a client holds their breath, takes shallow/ineffective breaths, breaths too quickly for the intensity, etc.
There are a lot of theories on breathing technique and I don’t know that I am qualified to debunk them all. But I have known a lot of elite athletes who never had a single bit of coaching on breathing and can do amazing feats of athleticism. A few who were given breathing advice that proved to be detrimental to their performance. And a few that swear by this technique or that technique.
I have spent a bit of time looking into breathing and decided that it wasn’t an area on which I wanted to spend too much effort. The most frequent advice that I find myself giving on breathing is for clients not to hold their breath and to just breath in and out as naturally as they can. If they have trouble with that, I go with ‘breath out on the greatest effort phase of an exercise and during the least effort phase’. But that can be different for each exercise and each client, especially in the beginning of exercise programming. It almost always improves as time goes on without too much time spent focusing on it.