There’s no such thing.
You’re either fake or authentic. There’s no way around that.
Whoever you see referring to “fake authenticity” is off the mark —by miles.
Because if you can’t call fake by what it is and need to put “authenticity” to complete the idea, you’re also buying into the belief that authenticity can be faked.
Like a cold heat, or like flat-earthers around the globe.
After all, you being you is not about even being authentic —in a professional/business setting.
Authenticity is not “do what you feel like doing,” because that’s unlikely to be useful. — Seth Godin
You being you is staying true to your core. And that’s what reflects authenticity —or distinctiveness. What makes you stand out.
And for that, there’s no need to fake.
Nor “fake it till you make it”.
Because when you fake it, people smells it.
Like the stench of desperation.