Askerisk next to connection bars what is it about

Could you provide a screenshot of what you see at Settings > Focus?

Smart Activation is used to automatically turn a Focus Mode on based on your activity and it is probably best to leave it off. I don't find Smart Activation helpful at all.

This may not be related to the Mail problems you are experiencing, but could be the reason for the asterisk you are seeing. For the Mail problem, go to Settings > WiFi and turn it off so you can test it the save thing happens when using your Cellular Data. If it works on Cellular, then you know that it is related to the WiFi connection and we can further troubleshoot that.

Ok, thanks for the screenshot. Do you have a Custom Focus? The asterisk is one of the symbols you can select for a custom focus. Go to Settings > Focus and see if it listed there.

Is it an asterisk or the spinning circle that represents network activity.

Are any of the Focus modes listed at Settings > Focus represented with that same asterisk icon?

Perhaps you could provide a screen shot.