Beta watchOS updates are available only to paid participants in Apple’s developer program. You can, however get public release versions of iOS, macOS, and tvOS betas. Those typically follow within a couple days of the developer beta releases.
Apple also released macOS High Sierra 10.13.5 developer beta 5 today.
If you’re registered in Apple’s developer program and interested in testing watchOS 4.3.1 beta you can check it out at the Apple developer website.