There are cryptography primitives allowing you to privately make an intersection of the certificates you have and the providers the site would trust and compute a kind of score while not exposing any of your certificates or which providers trusted you amongst them. (the only thing is that a website could extract the knowledge that one specific provider trusted you if they only trust one, but that could probably be fixed with a better protocol that the one I have in mind).
There are cryptography primitives allowing you to privately make an intersection of the certificates you have and the providers the site would trust and compute a kind of score while not exposing any of your certificates or which providers trusted you amongst them. (the only thing is that a website could extract the knowledge that one specific provider trusted you if they only trust one, but that could probably be fixed with a better protocol that the one I have in mind).