Works great!

Can you add a dark mode to it? Either make it black with white text by default, or add a dark mode toggle? That would be awesome!

Another thing would be making the download list tab specific. To add to that, I've found that using the extension popup to see the list and download files from there is much better than the floating download button. It just gets in the way of everything, so I have mine disabled. You could remove that functionality completely, also as a way to reduce the potential confusion resulting from making the list in the extension popup tab specific. (Of course, that would require 2 "clear list" buttons - one to clear the list for the tab, and one to clear the list in all tabs)

To add to that, there could even be a toggle to clear the list of the tab in question automatically when it loads a new URL (or is reloaded)