Do you have an order number or serial number? I can't match your name or email to any order.
If the Quadstick has bluetooth, it is turned off by default and would need to be enabled before use. The bluetooth module is not really used for gaming. It has a generic game controller device mode, but it does not match any of the standard game controllers the Steam Deck is likely to recognize. The quadstick is primarily a USB controller. The bluetooth module can be useful in some situations, but it is not the primary way to connect things.
My guess for the best configuration for the Steam Deck would be to treat it like a PC in Steam's Big Picture mode, which can be operated with an XBox 360 controller and use the Quadstick in that USB emulation. There was an example of an XBox 360 configuration file on the Quadstick when it was shipped. See the printed list of game files that was in the box. The file number varies depending of what options were selected in the order.
Does the Steam Deck have a general purpose web browser that would allow you to log into a google account? You may be able to use the Add-on's Quadstick menu in a configuration spreadsheet to download new configurations.