No Sony said they were implementing 1080p and beyond, they never said they were limiting themselves to only 1080p. Also there was no indication that they were going to have to wait until the next gen hardware became available to implement a resolution boost, that could very well come before next gen hits.
The PS5 hardware will be capable of 8K resolutions and since it'll be HDMI 2.1 compliant it'll also be capable of doing 120 FPS if they want it to (not necessarily together). My guess is we'll get 8K games that're upscaled using a variant of checkerboard rendering.
As for Stadia, there's no timeframe on that at all, it's just a bullet point until Google decides to give more info.