SteamVR manages the standby/sleep/on modes of Base Station automatically whenever you're using a native SteamVR headset, however if you don't, you can't use this as you're unable to access the Bluetooth/Base Station settings in SteamVR, there is a fix for this using a Third Party Software that lets you manage your Base Stations manually/automatically, however this option does add more to your overall cost, so what I suggest here is the Steam application itself detecting whether the user's system has Bluetooth so SteamVR allows the user to have access to its power management.

Another option would be for the Steam application itself to handle Base Station power management natively whenever SteamVR starts or stops, provided the user's system has access to Bluetooth.