Hello Woody,
Thank you for your question and for reaching out with your question today.
The behaviour you described, where a Microsoft Copilot icon appears on the Windows taskbar and prompts users to update Office, is not a standard behaviour for Office 365 updates. It's possible that someone in your organisation has made changes to the Office update settings using the Microsoft 365 Admin portal or deployed a custom solution that triggers the update notifications.
By default, Office 365 updates are usually configured to be installed automatically in the background without any user interaction or notifications. However, administrators have the flexibility to customise the update settings based on their organisation's requirements. They can choose to enable or disable certain update options, such as displaying notifications to users or allowing users to install updates manually.
To investigate and verify the update behaviour in your organisation, you should check the Microsoft 365 Admin portal and review the update settings and configurations.
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Best regards.