anything automated goes straight to specific folders for those categories. Very quickly identify stuff that’s noise and put in rules to move it out of your inbox. Sure some stuff you might need, but anything that’s corporate spam needs automating away.
use (and create if necessary) the right mail groups so your whole team, project partners, whoever see the right emails and ask people to use them.
add a VIP rule to highlight emails from the boss, VP, anyone you know you want to read right away
be clear with people on how to reach you. If you prefer Slack for immediate stuff, tell people. It’s fine to be clear that email is for less immediate consumption, or non-conversational stuff. Slack is far better for collab.