Use a Windows 10 computer on the same Bluetooth adapter to pair with the controller. It must absolutly be on the same Bluetooth adapter, i.e. the same computer (can be inside a virtual machine with Bluetooth passthrough) if it’s an internal Bluetooth adapter, or the same Bluetooth dongle. Then, you can get the pairing keys and install them within your Linux Bluetooth system.
I have a Elite controller v2 and I wasn’t able to pair it on my laptop with arch, indeed I had to follow this instruction on their wiki https://atar-axis.github.io/xpadneo/#troubleshooting