I created a new project, installed Newtonsoft.Json and added a class.
If you have your class file open, copy your Json data and choose Edit -> Paste Special you will see both the options:
If you have some other kind of file open (e.g. app.config), you only see “Paste JSON as As Classes” (and it’s greyed out)
It does seem a bit flaky though – sometimes I had to recopy the data before it would show up.
Try a) recopying your data b) playing around with what windows you’ve got open c) reinstalling the extension