I'm confident this is not a bug, but it's by design.

https://quickbooks.intuit.com/learn-support/en-us/reports-and-accounting/every-time-i-email-an-invoi...

In other posts I see them saying that XXXXX or YYYYYY provider is not supported. Seems to me that QB doesn't want to save ANY passwords. When you use Gmail it connects to your account as a third party app. So, they are still not saving passwords but just making a connection to Google. Same idea with Outlook/Hotmail. It seems like it has to be on the drop down list of providers to save the password, whereas "Others" doesn't because it's simple SMTP and they don't save that password.