I think jealousy is ore likely to occur in a new relationship than a more established one. You're not afraid of losing your long term partner because you know he won't leave you. However you're not so sure about the new one.
One thing is that he seems to be monogamous. If he is, then, and he finds someone else, who is also monogamous, there is the risk of hm leaving you for that other guy. With a poly partner there is less worry because you know that even f they find someone else, they have no reason to leave you.
And as I said, it's less established. With your long-term partner, leaving you means a lot more due to your history. With this new one, it looks like he could cut ties rather easily and be done with it... He doesn't even tell other people he's with you! It's like officially, your relationship doesn't even exist. I'd be insecure too!
I think it makes sense in some way to be more jealous of people when you know they're not looking for other partners. Provided you're not secure with the fact that they won't find anyone else, I mean. Because if they do meet someone, contrarily to the people who are looking, are prepared, have planned for it and know they'll stay with you, these people will be taken by surprise and might choose the new person over you.
I think you need to work with him at strengthening your relationship. You could tell him that you mind his status is shown as single, because you feel he's trying to hide you or something. That could be a beginning.