I’ve had interference using the embed approach because it’s wrapped in a div tag. A more reliable solution (but still a non-standard implementation) is adding GTM to the custom footer which gets inserted before the closing body tag. The problem with this is it does not fire on partial page loads.
Best solution so far is manual insertion after export (if you are hosting externally) right after the opening body tag. Even though I export all my sites, this is still a pain and I wish Webflow would enable a new custom code field for right after the opening body tag… or offer code insertion without the divs.