Building my own handheld game? Game engine and SoC advice?

I'm curious if anyone has messed around with both SoC (arduino, esp32, etc.) and game engines like Godot, Gamemaker, or Unity, and have tried porting their game to work on an SoC? That digital pet thread kinda sparked off a desire to make my own handheld tamagotchi, both designing the physical device and developing a simple game to be played on it. I've some experience with Godot, enough to know that creating a digital pet game wouldn't be an unsurmountable task, but I've never messed with SoCs and I'm not sure which hardware (and their respective limitations) and operating systems would be suitable for running a simple 2d game. How would I even port a game over, etc?

If anyone has any ideas or suggestions, I'd be thankful to hear them!