I'm surprised they don't have a bugs thread? In BL3, I noticed I had to change the brightness setting every time I logged in. The game remembered all settings but that one. At the time, I thought it was a BL3 issue but I'm noticing the exact same issues, just with the one setting, brightness, on ESO, too. So clearly its a Stadia issue not a particular game's issue.
Are you using a TV with a chromecast?
Is it the specific input, and does your TV remember settings per input?
If not, can you provide a little more information?
I have Chromecast but have never used it. It's on my 2017 Mac Air which I cable into directly (USB via Stadia controller) to play on Stadia. To be very specific, any game's settings other than those dealing with visual brightness are retained. All games I play (BL3, ESO, Red Dead) do not retain the brightness setting.