Dear Paul,
We appreciate you spent time doing tests and share with us the result. We do understand it has caused inconvenience to your work and apologize for it.
To further narrow down the issue, if you open an Office app, such as Word, click your profile image, do you see SharePoint in the list(as shown below)?
If yes, click it, check if you can see any SharePoint folders (as shown below). If yes, hover over it and click X to remove it.

If the pop up still appears, we do understand the inconvenience caused and apologize for it.
The best way to troubleshoot the situation further is reporting it to the related team and let them remotely assist you, check the environment, collect logs and help you find root cause.
Therefore, we sincerely recommend you contact your Microsoft 365 administrator, follow steps in this article to raise a support ticket: Get support - Microsoft 365 admin | Microsoft Learn
For reference: How do I find my Microsoft 365 admin? - Microsoft Support
If you have a personal Microsoft account, you may contact related team from this page. Firstly describe the issue and click Get Help, then click "Contact Support" on the bottom, select products and services(Microsoft 365 and Office), Category(Technical Support), confirm, then you can chat with a support agent in your web browser.

The support team has higher permission to remotely assist you, they have more resource than us. This would be the most efficient way in handling this case for you.
Thanks for your cooperation! I hope that you are keeping safe and well.
Sincerely,
Tina | Microsoft Community Moderator