I can't test Outlook 2016 but our Teams is updated to version 1.6.00.22954. So you might check if there is a new version of Teams available - though your version should have the fix...in theory but Outlook 2016 may not be covered for whatever reason.
Also as some noted in the thread above, for tbshooting, in Windows File Explorer navigate to %userprofile%\AppData\Local\Microsoft\TeamsMeetingAddin to check the versions of the add-in. There should always be two versions - the previous one and the newest one - there shouldn't be any need to delete the older one.
Check the meeting-addin-install-logs.txt in this folder, scroll to the bottom for the recent entries, and note any error. In my log the last entry is "2023-08-17-06:05:13.083 PM Version 1.0.23213.1 of the meeting add-in is now installed".
When updating Teams, you do need to close and restart Outlook if there is a new version of the add-in. Otherwise Outlook will continue to use the old version until its restarted.