I had configured an Incoming Webhook on one of our Microsoft Teams channels, but noticed it stopped working recently, and also I am no longer able to find the Incoming Webhook in the list of connectors:
What command would I need to have our Administrators run or what configuration would I need to apply to get this to work again?
As @wajeed-msft notes, this is happening because your administrator turned off access to external applications.
Assuming "Allow sideloading of external apps" is also turned off you'll get the list on the page you found above. If you scroll through that list, you will see "Incoming webhook" listed.