From the Stanford IT site:

4:10 PM: University IT engineers continue to monitor updates from Microsoft. They reported initial progress but have acknowledged setback in the deployment of their remediation. Mail to M365 accounts continues to fail at this time.

1:27 PM: Users continue to experience delays sending and receiving email due to a widespread Microsoft 365 (M365) outage. University IT teams are actively monitoring the issue. Updates are provided on uit.stanford.edu as information becomes available. Thank you for your continued patience.

12:55 PM: Users may experience delays sending and receiving email due to a widespread Microsoft 365 (M365) outage impacting several M365 services. University IT teams are actively investigating the issue and will share updates as more information becomes available.

The problem seems to cover "thousands of Microsoft customers," not just Stanford.