You have to wait longer to get the new OS for series 1-2 watches. I upgraded from the series 2 to the series 4 recently and boy is the 4 so much faster and nicer!
I have Series 2 also, and iOS 13 on iPhone 8 Plus and when I launch the watch app on the phone it goes to checking update and never stops... if I try and cancel it says “reset watch which will unpair” or “continue update” and never stops just spinning wheel. So until the release of watch OS6 for series 2 I can no longer use the watch app on the iPhone???