I tried to make a pretty extensive case for it at https://overreacted.io/open-social/#open-social, I'd suggest reading it with an open mind to form an opinion. I think there's quite a few interesting aspects there, like apps being able to "piggyback on" data from other apps.
I wouldn't call AT a "reinvention" of the web, personally I see it as a minor bump that codifies some conventions that let apps interoperate while keeping the source of user data outside those apps. New products can be started from data of other (even defunct) products and remix it. That's pretty powerful.
I'm still not really convinced. Look at it from my perspective: I have my website, BSky isn't compatible with the web, therefore I would have to provide two different versions of all content I publish to satisfy someone else's protocol. It's very annoying. It would be simpler and more effective if it was built on existing web technologies. The only actually new things AT and BSky provide is a signature scheme for content, and the ability to store replies, follows, and likes. You manage most of that in as a few HTML meta tags à la OpenGraph. The other parts of it already exist, those being a web-page designer and an indexer.
I wouldn't call AT a "reinvention" of the web, personally I see it as a minor bump that codifies some conventions that let apps interoperate while keeping the source of user data outside those apps. New products can be started from data of other (even defunct) products and remix it. That's pretty powerful.