So did we get any new mathematics out of this, or just solutions to problems without new techniques or insights? I haven’t been able to keep up with this or read the writeups you mention, genuinely wondering since this seems to be a central concern of the math community

It's only been a month and people aren't that fast, but I think yes. Analytic number theory and complexity theory were stuck on the lack of progress on certain questions, that is now unstuck.