so...its kinda like Stadia (was?) except you can use it with "any game service" like Steam?
Right.
If so, I can imagine that it would also perform like Stadia reportedly did, and some games (like FPS) the lag might be intolerable to some users?
Right. Basically all streaming services suffer from lag, there is always lag if you transfer input and output over an internet connection. And if it will never become zero until the theory of relativity will be proven wrong. How much it does affect your experience, depends on how vulnerable you are for lag and of course your internet connection.
I additionally assume "input lag" is overestimated. It's a hype. Most people complaining about input lag will still not notice anything, if the input lag is below... 20 or 30ms. It's measurable, but not really noticable.
The input lag is there anyway. That's exactly what you can see in many multiplayer games. Your client just does "estimations" for online games.
E.g. you trigger a shot and your client calculates it's a hit it shows blood. However your client only transfers your current telemetry to the server. The server then calculates if it is a hit or not and answers with the result. Your client can only determine if it REALLY was hit when he received the answer from the server. Sending, calculating on the server and receiving the answer takes time. ALWAYS. That's the lag, even if it is not video streaming. That may result in your client showing a hit, but the server calculates it isn't. Then you see blood, but you didn't hit the enemy. Thats even more confusing, because you "see" a hit, but you didn't hit. That's a very common problem for any online game, and so the lag is there anyway.
If a game is implemented the other way so that only the client does the hit calculation and the server trusts this information, your game is free for client hacks. So you shouldn't wonder about cheaters. Also a common problem, because some games do it that way.
Most well known and obvious problem is also: If there is only one player with bad ping, you will see his position delayed or even jumping. That makes accurate targeting also impossible.
So if playing online, there is lag anyway. One way or the other. It won't vanish. Since it is there anyway, lag is only relevant if you play singleplayer via streaming. E.g. a bullet hell game. But i still doubt most people will even recognice the lag if it is low enough.
The only situation where i really recognized input lag was, when i played guitar hero (which is highly addictive to input lag) on PS2. If i used VGA output instead of Video, my TV caused some input lag. The game provided a correction for that with testing mode. I ended up with setting it to -180ms felt accurate. I can't tell if -160 oder -200 would have been better, couldn't feel a difference. And it's the same with online gaming, no matter if it is just client-server-communication-online or streaming-online.
If you are interested, just test it. GFN can be tested for free. Shadow provides cheap testing accounts. Don't know about stadia. Afaik there is also a free version that at least allows testing. Lag is not really affected by streaming resolution or quality.
If you approach it with the thought, it's impossible anyway and has to be bad, of course you will find any nitpicks. Take this apart and just test it.
If you are not playing high level professional tournaments, i doubt you won't notice anything.
There is a lot of imagination out there. I've already proven MANY people wrong that claimed to definitely see 144fps over 60fps. But when testing them, without knowing them what display and framerate it is (in a game) they couldn't tell anything.