SmartThings would like to support nest, that’s why they keep applying for it, if only as a marketing position.
But as has been discussed in the past by SmartThings staff, nest will not approve them because the SmartThings platform allows control of too many features of the nest device and nest likes to limit the features its “works with” partners have access to.
Indeed, the original custom build integration that was used in the community back in 2014 was a violation of the nest terms of service, and that statement is still on the official SmartThings support website.
https://support.smartthings.com/hc/en-us/articles/204733384-Does-SmartThings-work-with-Nest-
Fortunately, since that time the community has created a different integration method, “nest manager”, and that one does not appear to violate the terms of service. Which is good. But it still doesn’t meet the standards of the “works with nest” program, so it can’t just be officially adopted by SmartThings and solve the problem. But individual consumers can still choose to use it.
IF you Haven’t used custom code before, here’s the FAQ for that. It’s pretty straightforward, basically you’re going to copy someone else’s code and paste it into your account.
As far as where you get that code, the community – created wiki has a set of quick browse lists which can let you quickly find custom smart apps and device type handlers you might want to try. The ones for nest will be on the HVAC list. “Nest Manager” is the most popular for this specific purpose, but it’s good to know that the list exists once you start looking at other things as well. 