Sdl.ProjectApi is not public assembly that's why you're unable to use it in Trados Studio plugin. As far as I know Studio checks if plugins are using non public assemblies and throws this error. Standalone application won't check if assembly is public or not that's why it works.
You can check list of public assemblies here: c:\Program Files (x86)\SDL\SDL Trados Studio\<your version of Studio>\pluginconfig.xml
and find more details in this post: community.sdl.com/.../2114