I’m in the Discord for Loops, but not affiliated with it. The dev said they’re rate-limited by their email provider, so it does take a long time to go through the queue. The queue is also split between Pixelfed and Loops, since they have the same developer, so that slows things down even more.
It took about three days to get my invite as well, but it may be a bit faster now since I think the initial surge of signups has tapered off a bit.
They’re still working on it. All the dev is by a single guy, who also runs Pixelfed. He says he’ll be open-sourcing the code soon so more people can contribute and help get things going, but he wants to finish getting the web interface working first. And apparently he’s been spending a lot of time keeping everything online during the surge of interest, which has slowed everything down.