iPhone SE and WatchOS 6

How was your update? I regret updating my watch 4 to OS 6.x.x. It worked flawless on OS 5. I am waiting for my carrier's engineers to help determine whether the carrier, watch, or the iPhone SE is the source of cellular/LTE connectivity issues. If they don't find the source, then I'll use Apple Care on the watch.

Yes. Your iPhone SE is capable of running iOS 13. After installing iOS 13, you’ll be able to use the Watch app to download and install watchOS 6 on your Series 4.