for anybody who is saying that it tells them to log in even though they already have (Grammarly is active, but key features are missing. Sign up now to unlock the following'.) go into your gmail and try typing the little icon should appear on the bottom right corner of the email you are typing click it and follow through the instructions, after that it should log you in.
I know this is complicated and they should fix it but, it worked for me and hopefully it does for you too.
Says that I need to sign in, and if I try, I am signed in, but then nothing happens, and it still says I am not signed in? I tried to search their support page for solution - nothing. But many people are having the very same issue.