Having the number and this twitter account isn't acceptable even if they are not speaking right now. It all has to go, I thought cutting contact meant get rid of everything
I agree with you.
I'd go further and say that the total cutting isn't enough to put your marriage back in a good place.
Cupcakes.... look at it from the perspective I'm about lay out.
He tells her if he was happy with you, he wouldn't be with her.
In your discussion you didn't include plans of how the two of you might try to reconnect and be happy as a couple.
It's purely about staying together for the children.
Essentially, nothing has changed, apart from you both expressing unhappiness.
From his POV, he's still missing the happiness he doesn't have with you.
He might not be getting it from her at the moment, but he could in the future. So he keeps a way of contacting her, as a glimmer of hope. He's clinging on.
With you, I'm not sure if he sees that he could be happy again.
That's a crucial element of your discussions that's missing. It's not all on you though, as he has a responsibility to be an active part of the future of your marriage.
He just seems so conflict avoidant about being honest with you. Perhaps if he was honest, instead of you guessing, assuming and analysing his behaviour, you'd be under no illusions about where you stand and how he feels.
From everything you've written, neither of you come across as being able to be honest or vulnerable with each other and that's usually because, you don't feel enotionally safe with each other.