peter-supply is the addin visible in the outlook addins, but disabled? Or is it not visible?
We got it working on Office 2016.
Also check teams classes. We noticed that sometimes registration is not done correctly (mainly when uninstalling old teams and installing new teams).
HKEY_CURRENT_USER\SOFTWARE\Classes\TeamsAddin.FastConnect
HKEY_CURRENT_USER\SOFTWARE\Classes\TeamsAddin.FastConnect.1
HKEY_CURRENT_USER\SOFTWARE\Classes\TeamsAddin.Connect
HKEY_CURRENT_USER\SOFTWARE\Classes\TeamsAddin.Connect.1
And if outlook addin is visible in the addin section in outlook but disabled, verify the path to the addin DLL file in the following regkeys:
HKEY_CURRENT_USER\SOFTWARE\Classes\CLSID\{19A6E644-14E6-4A60-B8D7-DD20610A871D}\InprocServer32
HKEY_CURRENT_USER\SOFTWARE\Classes\Wow6432Node\CLSID\{19A6E644-14E6-4A60-B8D7-DD20610A871D}\InprocServer32
HKEY_CURRENT_USER\SOFTWARE\Classes\TypeLib\{C0529B10-073A-4754-9BB0-72325D80D122}\1.0\0\win32
HKEY_CURRENT_USER\SOFTWARE\Classes\Wow6432Node\TypeLib\{C0529B10-073A-4754-9BB0-72325D80D122}\1.0\0\win32
HKEY_CURRENT_USER\SOFTWARE\Classes\TypeLib\{C0529B10-073A-4754-9BB0-72325D80D122}\1.0\0\win64
HKEY_CURRENT_USER\SOFTWARE\Classes\Wow6432Node\TypeLib\{C0529B10-073A-4754-9BB0-72325D80D122}\1.0\0\win64
Also the user has to signin to teams at least once before button works. AddIn usses file %localappdata%\Publishers\8wekyb3d8bbwe\TeamsSharedConfig\tma_settings.json for some settings.
At start of outlook there should be some logfiles for the addin in %temp%\Microsoft\Teams\meeting-addin that can be used for troubleshooting. These files only appear if it actually loads the addin DLL file.
When teams is launched there should also be a logfile "%localappdata%\Packages\MSTeams_8wekyb3d8bbwe\LocalCache\Microsoft\MSTeams\Logs\tma_addin_msi.log" for the installation of the addin in the user profile.
Also take a look at https://answers.microsoft.com/en-us/outlook_com/forum/all/new-teams-meeting-add-in-is-missing-from-outlook/8e9531ce-3852-4a5b-ac1f-5a3f5d3bacf0?page=11. It could be that user MSI installs are disabled by policy?
Hopefully these things can point you in the right direction