Is the Lutron SeeTouch supported?

Yeah, that’s a nice device. Unfortunately, that’s from the model line for professional installers, RadioRA2, which uses the Lutron “connect bridge.” The SmartThings integration is with the Caseta line intended for do it yourselfers, which uses the Lutron “smart bridge.” So not currently compatible.

There are a few options for multibutton devices that will work with SmartThings. See the following thread, which covers both wallmount and handheld options: