What did I photograph around 6 AM on April 27th, 2021? Supermoon plus comet?
Having seen the extra photos, this is certainly a cloud.
It is a high altitude cloud: a fragment of cirrus composed of ice crystals.  These are aligned roughly horizontally, and they are catching the light of the moon. This is why the region of the cloud is more highly lit than the parts to the side: a sun-pillar (or moon-pillar?) effect.
Its movement over the course of a few minutes also indicates a nearby object. It is not a body in space, as astronomical bodies are so distant that they appear to move only very slowly.  One very simple rule is &quot;if it moves or changes, then it isn't astronomy, it's meteorology or technology&quot; This isn't quite true, but very few astronomical bodies can be seen to change position over the course of a few minutes.