Need advice

Excuse the vague thread title, I'm going to be going into some specifics here so wanted to keep the title vague. And sorry for the long read, thanks in advance to anyone who can help.

Background:
I'm a gay guy in my late 20s. I've been with my boyfriend of the same age for just under a decade. We've had our ups and downs like anyone but by and large it's been a good relationship and I feel like we've been through a lot of life together. We even broke up for several months a few years ago when we realised we'd gotten in deep very young, saw other people, took some time to find ourselves, and decided we wanted to be with each other again.

We moved in together a year ago. Unfortunately things started to go downhill after that. He was finding work very tough, was being treated quite badly, and ended up having to take some time out. He saw a doctor and was diagnosed with depression and anxiety, for which he took medication for several months. He also started seeing a counsellor on/off but I think he was just too worn out to engage with counselling.

He's doing better now, has got a new job and has come off medication. At first he enjoyed the job, but lately he's been getting very stressed again and is starting to show some of the symptoms that needed medication last year. This is despite him being treated a lot better in this new job. He's seeing a different counsellor (who is also a psychotherapist) now and really does seem to be trying to engage with it, with some positive results, but I think it's going to be a long process.

This much I can deal with. It's a little scary because I've seen the toll mental health problems can take on relationships over decades, but I'd stick by him if he had cancer so I'll stick by him through this.

The issue:
The issue is that I have discovered he is on a dating/hookup website. I've known this for months (saw it on his phone). At first he was only chatting on it, and outright refusing any sexual contact with anyone else. It disappeared from his phone, but I kept an eye on things, creating my own account that I used solely to monitor his (I hated myself for sneaking, but he was only chat and I didn't want to put him through the mill when he was already struggling with his mental health).

Recently he's back using the site. After a lot of hesitation, I started chatting with him on it, disguising my identity. We arranged to hook up for sex - he thought this was with someone else. I stopped chatting to him after that and obviously the hookup never happened. This was a few days ago. He still doesn't (I think) know this was me. Since then he's been overcompensating, trying to do extra things around the house, reiterating that he loves me more times than usual, etc., which I'm putting down to guilt.

Where I'm At:
I have no idea if this was the first time he arranged a hookup like this, or he would ever actually have gone through with it. While the idea that he may be having sex outside the relationship upsets me, and comes with physical health concerns for me (which I will be dealing with), it's not the main thing bothering me. I feel like that's the symptom of something that has gone majorly wrong in our relationship.

I love this guy. I want to save our relationship. But I don't know how to approach it. I know I need to confront him on this. But I don't know how or when. I want to be able to support him with all the other mental health stuff he's going through, and don't want to dump a massive relationship problem on his plate that going to have us at odds (even with a view to working together to solve it.) However, I'm aware that ignoring this isn't going to work. I can't have a sexual relationship with him while my health is at risk (not that that happens much anyway these days given the mental health issues, but infidelity means ending that altogether for now). And the stress of keeping a lid on it will eventually take its toll on me.

I'm also scared as to where this might lead. I want to forgive him and work on the relationship. But I'm afraid to. My father cheated on my mother when I was a kid. He wasn't depressed but did have very low self-esteem, which my boyfriend has said is also a problem for him. There's also a lot of similarities between my father's family of origin and my boyfriend's (although I may just be hyper-alert to these similarities). My mother forgave my father, for all the right reasons. Ten years later he did it again, only this time was incredibly vindictive about it and did everything he could to not only destroy the marriage but to leave her totally destitute financially afterwards. She's 60 and I doubt she'll ever find a partner again. If I'm to break up, I want to do it in my 20s, when I'm still young enough and self-sufficient enough to get back on the horse and find someone else I can spend my life with.

OK, long read over. If anyone got this far, thank you, and all advice gratefully received.