Steam Deck natively recognizes the PS3 controller. Simply plug it in via USB, wait for Steam OS to recognize it, then unplug USB cable and it will work over Bluetooth without needing
PS3 Controller with Windows | Austin Tate's Blog
Amazon.com: Controller 2 Pack for PS3 Wireless Controller for Sony Playstation 3, Double Shock 3, Bluetooth, Rechargeable, Motion Sensor, 360° Analog Joysticks, Remote for PS3, 2 USB Charging Cords, Black : Video Games
How to use a PS3 controller on Windows 10
Amazon.com: PlayStation 3 Dualshock 3 Wireless Controller (Black) : Video Games