Its not listed as Switch compatible. I would go with the first one from your original two links or one these;

https://www.amazon.com/Bluetooth-Nintendo-Switch-Wireless-Transmitter-Headphones/dp/B07Y1FJ483/

https://www.amazon.com/Skull-Co-AudioStick-Bluetooth-Transmitter/dp/B08DZRJD2N/

https://www.amazon.com/Genki-Nintendo-Switch-Bluetooth-Adapter/dp/B07JZKXSQT/