The small USB stick shown in the photo is a USB 2.4 GHz wireless adapter supplied by 8bitdo, called USB Wireless Adapter 2. It allows the wireless controller to be connected to devices such as a Windows PC or Nintendo Switch via a 2.4 GHz connection, providing a stable, low-latency connection.

As for the Bluetooth connection, the controller can actually connect directly to the Nintendo Switch or Switch 2 without using this USB key. Bluetooth connection is natively supported by the controller for these consoles. However, using the USB key provides a more stable and responsive 2.4 GHz connection, particularly on PCs, and offers additional features via the Ultimate Software, such as advanced customisation of buttons and profiles.

In short, you can connect the controller directly via Bluetooth to the Switch without the USB key, but the key is useful for an optimised connection and advanced options on certain devices.