I had the Warzone black screen thing once as well, alt tabbing fixed it for me too. Not seen it since touch wood. I have a feeling its a game issue tbh since I have some weird artifacts too (bright light flashes see YT video below) at times on the 4090.
I remember Warzone 1 had these sorts of bugs too periodically.
Using AMD here, but boot times are exactly the same for me on both GPUs. Since the XTX is fairly new, have you tried updating the BIOS and are you using UEFI mode?
I'm using Edge not Chrome, but don't see the mouse cursor disappearing. Have you checked to see if you are using the latest build of Chrome?
If you have not yet tried it, you should move to Edge. Better in everyway and a much lighter system footprint vs Chrome. Plus all these performance options available in the system menu.