Have you sent a calm message that is not pleading but just a reminder of what was agreed about sulking. Something like ' You are sulking again and we discussed it in therapy. Do you remember promising not to do it again? If this keeps happening, I am not sure we have a future. When can we meet to talk?'
Don't give an ultimatum, but make it clear you are rethinking your relationship, which you are. If he ignores that, it tells you a lot and maybe you don't need an ultimatum, you need to decide if you are willing leave and then just do it
If he does reply and starts communicating again, then don't let it go, remind him about how he said he would not do this again and how can you both work out a way that it does not happen again. Work out a stategy together - for example maybe you can both agree a reasonable for him to calm down if he is upset. For that agreed amonut of time you will leave him alone . After that time is up, if he does not contact you first you will text him to remind him his silent time is up and to arrange a time to talk.
Then when ihe ignores you again over something (and he will probably despite his promise not to as it is obviously a very ingrained habit) use the startegy you have agreed, this will make you feel more in control at the time he is ignoring you. If he does not keep his end of the bargain, to stop the silence after a reminder thatat the agreed time is up, then that really is time to leave - no ultimatum needed
Edit : sorry didn't mean to quote anyone ! Just addressing the op