My own order of the new Fire TV remote with app buttons has, unfortunately, been delayed so I haven't been able to test things out myself yet, but several of you have already told me that my Remapper app does work to remap the app buttons on the new remote.
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Introducing Remapper, my new app to reassign the App Buttons on Fire TV Edition Remotes
How to remap the App Buttons on Fire TV Remotes with Remapper (Updated April 2021), AFTVnews
Temp ROOT] - [BOOTLESS MAGISK] FireTV 3rd gen Cube (gazelle) ≤ PS7613, Page 6
Button Mapper: Remap your keys - Apps on Google Play
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How to Remap App Buttons on Fire TV Remotes