Hi Tom,
Thanks for your updates.
It seems like even in a newly created SharePoint site homepage, it is not showing the Copilot icon on the corner for you. In this situation, it is possible that there has some service deployment cache in the backend of your account or even the tenant (if it happens on other users as well). The efficient action is to contact the admin of your organization and request a free support ticket in Microsoft Admin Center.

Escalated Microsoft engineers there can make remote session with you and collect the HARs log from the backend to locate the cause of Copilot in SharePoint not appearing. Otherwise, they will also check if there have any settings in the tenant side that may prevented you from using Copilot feature in SharePoint Online platform.
For reference: Get support - Microsoft 365 admin | Microsoft Learn
How do I find my Microsoft 365 admin? - Microsoft Support
We are redirecting it to the right support channel to solve the problem. That's why we suggest you contact your administrator or your IT department. They can create a support ticket. Once your administrator or IT contacts them, the engineers will contact you back in 30mins.
Best Regards,
Mia