After working with my email provider, the problem appears to involve two-factor authentication (seems MS calls it "multi-factor authentication" in their documentation). Now, we don't have a **** clue as to why that's the case, but it looks like their
own Android app and their own Authenticator app, or any other MFA-supporting email client and authenticator app, just sometimes don't work on Samsung devices. I
think this may have something to do with Knox and/or giving Outlook/your mail client Administrative Rights to your device, but it's my device, so 1) No; and 2) It's optional in my case anyway and I aggressively do not care, so we didn't do any more
research or do something like create an individual "app password" to bypass it. I disabled MFA in my Office365 settings and the phone picks up emails fine now.
If you want a broad overview of MFA, https://www.eastfieldcollege.edu/services/onlineservices/pass/pages/set-up-mobile-for-email.aspx has general details that apply to any device connecting to an Office365 account (not just the school's), plus links out to
some MS troubleshooting and Office365 admin documentation.
tl;dr -- If you are accessing an account which uses 2FA/MFA using Outlook for Android, ditch the 2FA/MFA or ditch Outlook.
That said, anyone got a better free email client for Android that supports Office365? :/