You can dig into your settings and specify which mailboxes you want the Apple Watch to notify you with.
While you can use your Apple Watch as a sort of mini screen or surrogate write-mounted iPhone (when it’s connected to an iPhone itself), the small device does have its limitations. It also won’t automatically distinguish between incoming notifications, which means if you’ve got it set up to let you know about incoming emails the tiny screen might get really cluttered very fast.
