I have only a Steam Deck so I wanted to test on someone else's pc before responding. The Logitech controller worked perfectly on their Windows 10 laptop. I wasn't running through the itch client there but I doubt that made a difference.
On the Deck, if I launch Revamped without the external controller attached, the Deck's built in controls are still behaving wrongly the same as the external controller does. It's like that regardless of whether the Deck is docked when Revamped is launched or whether the Deck is not connected to anything else.