Yeah, I went through all the normal troubleshooting options, different ports, different cables, usbc to usbc, usba to usbc, trying to setup wifi, restarting the app and pc and iron, &c.
But my main PC uses windows 11. Reading through other comments it looks like that could be an issue, so dug up an old laptop still on windows 8, downloaded the aixun app, and 1.09 installed first try
Which also looks to have fixed the shut down issue and the iron is working now.
... so tl;dr, can confirm the aixun app is still borked on windows 11.