In recent days it has been discovered that World of Warcraft will be getting controller support in its upcoming expansion Shadowlands. This was found by grayson and shows that gamepad support including keybindings for Playstation 4, Playstation 4 Pro and Playstation 5. Stadia, for the time being, has been pretty firm with games requiring controller support so this will remove this barrier for World of Warcraft to come to Stadia.
One of Blizzards community managers called KaiVax addressed the situation
There has been no official news on console ports coming but by adding in controller support this would remove a significant barrier in that regard. Stadia would be in an ideal situation to capitalize if WoW did come to consoles. With Stadia you could have the best of both worlds in that you could play on either PC with keyboard and mouse or through controller via a TV. What also adds fire to this is Google and Activision / Blizzards’ recent partnership with YouTube.
We will be keeping a close eye on the story.