Whereas thunderbird used to require a separate "Lightning" extension to handle invitations and calendars, as of approximately 2021 that is no longer the case, so this is NOT an extension or add-on issue.
With help from Emile LeBlanc and various web pages etc, I first tried various solutions including selecting "Display Attachments Inline" on the View menu (important), and setting "mailnews.display.show_all_body_parts_menu" to True in the Config Editor at the bottom of Preferences / General and then restarting Thunderbird (probably not important), but the problem remained.
What finally solved the problem for me, was to select View / Calendar / Calendar Pane / Show Calendar Pane, and then go to the Calendar Pane (e.g. with the button in the top-right), and first delete all calenders except the default "Home" one (perhaps not necessary), and then right-click "Home" and select Properties and UNCHECK "Enable This Calendar", and then click the emerging button to Re-Enable it.
After doing that, then I could see the full Teams invitations again! Phew!
Warning: Once you can see the invitations, then do NOT select "Don't show me these messages" for the Accept/Decline/etc buttons under the "More" pull-down in the message's top-right corner. Nor uncheck "Display Attachments Inline" under the View menu. If you do either, then it seems that the above problem will re-appear, and you will again need to disable/enable the Home calendar as above to fix it. (Indeed, this is probably what caused the problem for me in the first place.)