They recently gave certain devs early access and a lot of demos are only now being shared by people with followings

I've noticed this too. Maybe it's anecdotal, but it feels like an attempt to astroturf the dev community or drive up buzz. I can't escape the superlative-laden Tweets and articles about GPT-3.

API/Playground is in private beta, I guess more people got access to it and started showing results. And upon seeing these results people get excited and talk about implications, etc.

Like, generating code and solving math is pretty damn good for a model which is not trained for generating code and solving math. Few weeks ago people didn't know it can do that.

It blew up on Twitter a few days ago, and it's still in closed beta so people are eager to see what it can do.

Marketing campaign.