How the hell do you get by with that? I’m jealous. I’ve gotten pinged by my fucking EVP for not responding to questions in chat fast enough (non-critical, too!). At least no one gets on me for missing emails. I don’t even read those.
You have a company policy that allows that. For example, if anything is decided in Slack, it has to be "codified" somewhere else, like a wiki. Then you'll be able to justify not reading through all messages.