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The first thing that greeted me when I signed in (with my existing Prime membership) was an upload window titled "Drag photos and videos here".

Me too. But they do not state that video storage is free, only photo storage.

Adding .jpg/similar to the end of the filename normally allows you to store about anything small enough, I found. (I didn't check here though.)

Isn't a video just a sequence of photos ?

In a sense. But a video file also stores things like sound which is one of the things that make the file size larger.