DruConnold -
could it be that when a Microsoft 365 family account shares the same email address as a work account with a Business Basic subscription, issues arise?
Yes, I think that absolutely could the issue here. We've actually stopped accepting new Microsoft account creations with IMAP/Exchange/other 3rd party email addresses besides the core consumer ones - Gmail, Yahoo, iCloud, etc. If user@company.com is both a Business Basic commercial mailbox and the alias of a consumer M365 Family accounts, it is NOT going to get both a consumer and commercial license. It will choose to connect to either the business mailbox or the consumer mailbox object, and then only get that license.
My suggestion would be to remove the IMAP alias from the Microsoft Account, and set them up with a new Outlook.com alias. See: How to add an email address or phone number to your Microsoft account - Microsoft Support. Then add that outlook.com alias first, then the Business Basic license. Or if you are the IT Admin, I'd just update them to Business Standard and tell them to stop paying their M365 Family license. BS is cheaper than BB+Family.
If you have additional questions here, DM me with your email address and details.