I use two old Google Stadia controllers (RIP!). When the service shut down, Google reimbursed everyone for their purchases, so the controllers were essentially free to me. They also released a webpage-based service to convert them to Bluetooth instead of WiFi which is super easy to do.
The controllers are great and you can pick them up pretty cheap on eBay etc. now that stadia is closed. They work seamlessly with the deck.
I didn’t even know it had a gyro… Does the 8bitdo have gyro? And does it work well with the steam deck? I haven’t used gyro controls much in general but did find them super helpful for aiming when playing through Half Life 2 again on the deck itself.