It’s been a while since someone posted a request about Grammarly desktop app integration.
All topics are closed now:
Plus there are several topics about bugs with Grammarly, so it is kind of a long sad story by now 
And because there is no real issue tracker (and no connection between these posts and the issue) - no one is reading this story.
I’d like to use Obsidian for my English, but I believe that instant feedback is beneficial in that area, so having a tool like Grammarly, which can provide me feedback on grammar and word usage will increase the efficiency of my learning.
So, right now I’m using LogSeq, which has this feature. I’d like to try Obsidian for that purpose because at least I like to structure my notes with folders and in LogSeq it is a bit difficult.