Connecting Razer Pro Type Ultra to IOgear USB switch wirelessly

Hello,
I recently purchased a Razer Pro Type Ultra.

I have been using an IOGear USB switch to swap between my PC and Laptop. It worked great with my last wireless logitec keyboard, but I am struggling to get the Razer to pair.

I can plug the wireless USB dongle into either the PC or the Laptop and it works fine.
I can plug the keyboard into the switch via the USB cable and it works fine and can switch between PC laptop.

However, I cannot plug the USB dongle into the switch and use the keyboard wireless with either PC or laptop, via either bluetooth or 24ghz mode.

I have tried using the Razer pairing utility. It works when I plug both cable and wireless usb into the PC directly, but cannot detect the wireless when it is in the switch.

Is there just a fundamental incompatability between the wireless USB dongle and this switch? Does it need power that the switch can't provide?

Could some firmware update or specific order of operations resolve the issue?

I would really like to get this keyboard working with both devices wirelessly!

Thanks so much for your help!