I want to push back on something here, because I think you're describing a real problem but then diagnosing it wrong. The problem isn't that you have a professional self. The problem is that you're treating that self as something separate from your actual self, when it's not.
You say "the person in that headshot and the person with those glowing recommendations" is "carefully constructed." But here's the thing: you *are* professional. You *are* someone that people write good recommendations about. That's not fiction. That's you.
What I'm hearing is that you don't like the version of yourself that cares about professionalism and presentation. You'd rather be the loose, weird, funny version. Fine. But that doesn't make the professional version fake. It makes you someone with multiple genuine sides, and right now you're privileging one over the other as "more real."
Maybe the exhaustion comes from that hierarchical thinking - the sense that your "true self" is being suppressed by a false performance. But what if they're both true? What if you're just someone who cares about how she comes across in professional contexts *and* wants to be looser in private spaces? That's not a split personality. That's normal.
The boundary didn't dissolve because of social media. You dissolved it by deciding that every context should reveal your "true self." But that's not how being a person works. The boundary was always there. Social media just made you aware of it.