Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hello,
Teams add-in in Outlook only works for accounts with business tier license, not on personal account.
Also, if you are using a third-party email address as your Microsoft account alias/username, this will cause calendar sync issue. Your calendar feature technically is still with Google, not Microsoft. Teams doesn't have integration feature on Teams personal to sync your Google Calendar into Teams. When you send out an invitation from Teams calendar, it will be using a placeholder outlook.com address to send it, and it can show up in your outlook and Teams calendar, but not your Google's. However, when you receive an invitation and accept, it will only show up in your Google calendar.
To address this issue, you will need to give your Microsoft a proper outlook.com alias. And have users send invitation to this outlook.com address instead.
Go to https://account.live.com
Go to Your Info > Sign in preference, Add an alias.
Create new: this will allow you to use the native domain outlook.com to create a new alias.