One of the healing things that should be done is a removal of all the past and given he did not have your consent to share that personal statement of his affair and breaking of vows is this.
To be real is to get consent for relationship activities and therapy for why he cheated and broke the vows.
To be real would also mean he would come up with an action plan for how to support you in your growth and independence, and let you take the lead "in private" and way from the social media angle.
If he can't ... isn't all in or being real. He broke your trust not once but twice, and your sadness is because of his poor actions and the pain you feel.
I hope you heal and he does what it takes to be a real man and becomes authentic in becoming a real man with real masculinity and not that of a boy playing with his toy which happens to be you his wife.