This is just a concern I had with the client. Back during the good ol’ Reddit days, I get notified about a post/comment reply immediately when it happens. I have since left that website, and for some reason I don’t know why this isn’t a feature yet.
And yes I have tried Connect for Lemmy, I had major problems with that app.
The API endpoints? It is
instance/api/v3/user/unread_count?auth=TOKEN
And thisinstance/api/v3/private_message/list?page=1&unread_only=true&auth=TOKEN