Dear @RM,
Thank you for posting your question in the Microsoft Q&A forum.
As a moderator, I don't have the tools to investigate your specific account directly because this is a user-to-user support forum. Moderators and contributors, including external Microsoft employees, cannot directly intervene in Microsoft product features or access back-end systems. Our role is limited to providing technical guidance on reported issues, requests, or ideas. However, I will try my best to guide you as clearly as possible.
To help me assist you better, could you please help me answer a few questions below:
Is this the button you are referring to?
Could you please check Teams on the web to see if you are experiencing the same issue there?
If the issue persists on the web, it might be because the Global Admin of your organization (the person who manages all accounts) has blocked it. Even though the computer belongs to you, the account itself is managed by the Global Admin. In other words:
Your computer rights allow you to install software, delete files, and modify Windows. You currently have this level of authority.
However, your Teams account is a cloud-based service, and that account falls under the management of the Global Admin.
If the Global Admin hasn't enabled the 'Outlook Add-in' feature in the central control panel, that button will never appear, regardless of whether you have Admin rights on your physical computer or not.
So, please help me check the web version to see if that button shows up there.
With the additional details you provide, I’ll be able to pinpoint the cause.
I look forward to your support and response!