Gaming

So...I've been increasingly struggling to run the latest games, as the age of my 6 years old desktop is starting to show, and Starfield denying my GPU just pissed me. I know it's a bug and I can probably play it, but it's outright the minimum for this game, and so I'd like a refresh of the worst, or should I consider a full new desktop? I know the GPU is starting to show its age, but not sure the CPU is salvageable or you'd advice a new one... Here's a quick short summary of the computer:

-Mobo Gygabite Z170 K3 -CPU i7 6700 -2x8GB DDR4 2133 -MSI Nvidia 1070 8GB -SSD 1TB on the SATA port (I believe I can install an m.2 instead) -EVGA G2 750W

My questions...I believe these days an AMD card would be cheaper than an Nvidia, correct? What would be an equivalent to a 3070, or a 4070? More importantly...are they bigger in size (would it fit)? Do they take more power than my 1070 (will it roast my power supply?). Power would be a bit important, as I'd rather not replace all the wiring for the power supply, and electricity is becoming kinda pricey these days... I'm basically considering upgrading GPU and RAM, and considering if this would be a good upgrade or the CPU would then be a bottleneck (hence just throw it all and go for a full new desktop...I'd rather not).

Thanks!