About 4 hours a week back
An estimate from your team's last 4 weeks: about 412 messages a week. Sorting by hand took about 45 seconds each. Confirming a sorted message takes about 12. That is 412 times 33 seconds, or 3.8 hours a week.
Writing replies is not counted. You still write or approve every one.
Simulated in this demo: no inbox is connected and no message is sent.