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.
It’s not that complicated, it just hasn’t been done. Most apps just check every few minutes if there’s something to notify the user of.