the marriage counselor is of the opinion that, although she may have started down the road to infidelity, nothing physical happened.
Looks like this is true. Whoop-de-doo. (Should the be 'whoop-de-due to truly rhyme?) If the mc thinks you should therefore ignore her non-physical betrayal, my reco is to fire the MC. In fact, MC sees your M as the client that needs to be treated. Your M hasn't failed. Your W has broken your M, and your M can't be rebuilt unless your W accepts that. She doesn't. So IMO, MC is premature unless you find an MC who sees their work as getting your W to recognize that she is responsible for her A.
My reaction is that an EA is cheating and that I am the one who says what constitutes cheating on me. She gets to decide what is cheating on her.
Both of those statements are true, too. Whoop-de-doo-due.
If you genuinely accepted the 'friendship' as not a betrayal, OK. That's your choice. But you don't accept it. You see it as an A and as a betrayal (as do the folks here). You have a lot of very painful feelings, and you need to heal from that. You can heal with her, if she agrees it's an A and if she agrees to prevent future betrayals. You can heal without her. I don't see how you can heal and R unless you agree on what her friendship is.
My reco is to avoid any manipulation that corners your W. R is hard work, and it succeeds only if both partners choose it freely. If your W doesn't truly want it in her gut, I believe she will build up more and more resentment as time goes on, and you'll be unhappy.
What do you want? Do you want to spend the rest of your life together? The work you both have to do to R can build a really satisfying relationship. It's really nice to wake up in the morning next to the person you want to be close to, knowing they want to be close to you. That's open to you if you both want it enough to do the necessary work. But do you want that with your W? Do you think she'll do the necessary work?
Right now, she doesn't even acknowledge her A or how much it hurt you. She's not a good candidate for R right now.
At least that's what you describe.
Is a purely emotional affair no big deal? If I think it is a big deal and she doesn’t, am I still justified in my objections or am I just being hyper-controlling?
IMO, hell, yes, it's a big deal.
Justification isn't the issue at all. The issue is that you believe - as most of us here - do - that she has betrayed you, and you're in pain because you've been betrayed.
At some point you'll have to address the elephant in the room: is it worth staying with her if she doesn't change herself from betrayer to good partner?
Right now, IMO, you have to process your pain out of your body. That's going to be a lot easier if she accepts responsibility for her A.
*****
Bottom line: I think you're in touch with reality, and I urge you to ignore your W's and your MC's messed up views.