No problem, but a WiFi controller is a bit like reinventing a worse wheel

No problem, just pointing out that it would be unusual for a controller to have 5GHz WiFi. We are guessing what kind of device Valve is making.This device having 5GHz WiFi lowers the chances of it being a controller.

Bluetooth I understand and makes perfect sense in a controller. Is a very common way to connect a human interface device wirelessly. It is a direct connection and can be very lower power and doesn't need to transfer alot of data. Not only did the Steam controller support Bluetooth like you mentioned but i believe the recent Xbox and PS5 controllers support Bluetooth as well. I think even the Nintendo Wii controllers were Bluetooth.

WiFi doesn't make much sense in a controller when Bluetooth already exists. Unless the controller has features that would benefit using WiFI over Bluetooth.

For example I could see maybe an advantage in a steam steaming/steam remote play situation. Instead of a controller going Bluetooth to local device and that local device passing the commands to the remote device, the controller could talk directly over the network to the remote device saving some latency for a more responsive experience. But I don't know why they would pick 5GHz that is more of a higher bandwidth application as far as i understand. You don't need that for sending basic controller commands 2.4GHz would be more than enough. Maybe it has something to do with Latency if your 2.4GHz network is congested you could to go with the less congested 5GHz frequency.