Solved it on my side by setting the "Status" of the Identity property to "On" inside of the "Identity" menu of my logic app.

To do so in your logic app:

1. Navigate to the "Identity" menu in the left-side menu of your logic app
2. Set the "Status" property to "On".

Here is an image to where to enable it: Enable Identity in the Logic App's Settings

That's it. Refresh your logic app and it will start to work.