Sometimes it is hit-or-miss. I think it might have to do something with the AWS backend that sometimes fail to connect instantly. We plan to improve on this for next iterations.
I've built a couple of Flutter apps and one of them was Flutter web. At the time (from 2020-2022), Flutter web definitely wasn't mature enough. It was a challenge and last time I checked (earlier 2023) there were some serious issues.
However your app seems to load very quickly and I can't see any glaring performance issues, and that leads me to think that maybe Flutter web has improved significantly in the last year. I sure hope so!
If you still have the source code to those apps (ie not work related ones), you should update to the latest master and try the Flutter web performance again, especially adding WASM [0]. It might be interesting to see just how fast it is now.
However your app seems to load very quickly and I can't see any glaring performance issues, and that leads me to think that maybe Flutter web has improved significantly in the last year. I sure hope so!