Hey @Echosong welcome to the forums, really glad to have you with us. I can hear how much this is impacting you, and how worried you are about your friend. They have taken that difficult first step in seeking counselling, which means they recognise that they need that professional level of support. It can be incredibly difficult to see someone we care about really struggling, and not know what we can do to help. I think sometimes the best thing we can do is gently remind that person that we're here for them, and as you say, keep an eye on them. Another thought - you could always ask your friend directly what support would be beneficial for them, what they find helpful/unhelpful, stuff like that.
It also sounds like it's been weighing pretty heavily on you. You are not responsible for your friend's mental health, and we cannot force others to accept our support, even if it pains us to have to take that step back. I think you can trust in the fact that your friend is in good hands (and hopefully this counsellor is a good fit to help your friend to make progress; if not, you can always encourage them to try again with someone new - it's pretty normal for a lot of folks to try a few different professionals before they find the right one).
There's a saying, "One cannot pour from an empty cup". Taking the time to look after ourselves, and putting our own self-care first is incredibly important in being better able to support our loved ones when they're struggling. Do you have things that you can do to ensure you're looking after yourself? Everything from massages and bubble baths, to engaging in hobbies and connecting with loved ones, to practicing mindfulness and other coping strategies, all the way to seeking counselling for ourselves as needed, can make an incredible difference for our day-to-day wellbeing, not to mention our capacity to provide support to others.
Your friend is lucky to have someone so caring and compassionate looking out for them, and I hope you take the time to look out for yourself as well 😊