Isn't the whole point of notifications to make it apparent when someone has responded to your thread?
If it's truly async then just close slack until you're ready to talk, then open it back up and go through all of the red badges / white channels.
If you absolutely need to keep all notifications off and still want to read any thread replies, the very top channel in the slack app is called "Threads" and will show threads you've participated in or subscribed to, listed in chronological order based on most recent replies.
I have a lot of problems with slack (namely, performance and lack of solid video/audio calling), but threads are fine.
How does that help with noticing threads that someone created while I wasn't looking?
- you have your info pre separated in channels instead of needing to sort your emails into folders
- you can pin important data to the channel for future reference
- even sending small files is less complicated via a chat app
- you can get up to date just by scrolling up a bit
That's all I could think of in 2 minutes.