I admire your honesty of the affair as you could have left that bit out but chose not to. It paints the picture of why it’s difficult. Unfortunately, by having an affair on their mother, you’ve effectively had an affair on your kids too. It’s the harsh truth but if you treat it that way, then you may have more sorrow towards them.
Usually these things come with time, but it seems that 3 years is long enough. It’s time to reach out and own up to your mistakes and show them that you are still their loving father.
Also, in terms of the depression and anxiety, have you seen a doctor or anything about them? Mental health is a scary thing and I’d hate to here about anything bad happening to anyone. Please get that checked out. If not, there are ‘over the counter’ things you can take to ease the pain of anxiety.
Anyway, I honestly hope this all goes well,