I like to keep my email inbox as empty as possible: only containing emails that I need to follow up or action which is usually less than 6.
I find Slack can be overwhelming, particuarly Direct Messages (DMs) which build up in the sidebar over time – particularly in a large company. At a previous job I noticed my team lead would use the DMs like an email – open a new DM to someone to ask something, and as soon as there’s nothing more to do close that DM so the sidebar is nice and clean. I didn’t even think to do this but I love doing it now – I only have DMs in the sidebar that require my attention, all other ones aren’t there (you don’t lose history of DMs, clicking the plus ➕ and adding a DM to someone shows your previous history).
I recommend giving it a try to see whether it helps you stay on top of your Slack.