The native app is a replacement to the web app. As you mentioned, it lacks automatic rain delay and this feature will not make it to the native app (unable to run 24/7 and not ideal device for changes).
The new UI hasn’t been tested against the web app as it’s no longer in active development. It most likely has issues since every iteration of OSPi causes issues. This is why I moved to the mobile_app plugin to get away from these issues. The web app does not use this plugin (hence the failure).
Both can probably be run at the same time however they will fall out of sync. In other words, the apps assume one user at a time and don’t make frequent polls to the device to changes not done within the open app.
Hope that helps.