I don’t believe the Enbrighten Wi-Fi devices currently work through a direct smartthings integration.
Because they do work with Alexa, you could use an Alexa routine (not a SmartThings routine) as an intermediary and turned them on and off from smartthings using the method in the following FAQ. (The topic title is a clickable link)
So it’s doable, but sort of a hassle to set up.
Also, it’s only a partial integration. That may be all you need for a smart plug, but you should be aware that if you turn it on or off in any other fashion, including its own app, smartthings won’t know about the state change. And you can’t use that plug turning on as a trigger. But you can use smartthings as the trigger to turn that plug on and off if that’s useful to you.
You don’t need to have an echo device to make this method work, but you do need to have an Amazon account and use the free Alexa app.
Also, fingers crossed: if both companies do eventually add matter support then I would think it likely that these would be able to be brought into the smartthings app that way. But that’s probably a year off at least, and no promises.