@Noel Burgess -- Shoot. Seems as though you're right about the extension disabling the command altogether. Although the actions you mentioned are not the same as the ones that execute given the shortcuts I listed. The shortcuts I gave don't select an adjacent tab, but actually reorder the active tab up or down. As Yu noted, there is no such configurable Edge command, whether with the hotkeys I gave or an alternative.
It isn't a huge deal. When the shortcuts are enabled I'm still able to use CTRL+SHIFT+PGUP/PGDN in the web app to cycle through tabs in the app, but once I reach the left-most tab in the app and use the PGDN command again, Edge moves the tab down in the list. The opposite does not happen with the PGUP command, i.e. when I'm on the right-most tab in the app and use PGUP again the Edge tab is not reorganized. Given that it seems like something the web app developer could address.
Luckily, when the PGDN command reorganizes the Edge tab I can still use PGUP to move back up the tabs in the web app.
Thanks for pointing this out, and to @Yu Zhou-MSFT for the original suggestion.