...yea, I'm also getting the same exact issue?!
Since iOS 13, I am constantly seeing this icon in the status bar:
Its ALWAYS there and has only been ALWAYS there since iO13 (and I'm actually using iOS 13.1.1).
I checked in the Location services under Privacy, and figured out it was the native Weather app causing this :
When I turn this off, and I check the weather app on my Apple Watch, I get a notification asking me if I want to allow the Weather app to use my Location. Even when selecting the 'Whilst Using app' option, the icon seems to stay in the status bar of the phone?!
This never happened before - is this a bug in iOS13?