Screen Time Across Platforms

My kids each have a couple of potential ways they engage with screens. A shared family TV, one has an old iPod touch, there are a couple of older shared iPads (I plan to get each kid their own Fire tablet at Christmas this year and retire the iPads), and one has a Nintendo Switch.

Each of these devices has a way to limit screen time, but to help make my life simpler and give them more freedom, I'd like to find a way to give a total screen time amount across all devices. Get super into a new video game? Use all your time there. Into a series on Netflix? Use your time there. Or balance it across devices.

Is there an app that can manage this across different platforms? Any parents with pro tips on how to do this? When I get the fire tablets, I considered blocking direct access to the TV and having them stream from their tablet. It looks like there are some cross-platform solutions for iOS and Amazon. I can't seem to find anything that integrates with Nintendo though.

Also, if there are shared devices, are their apps that can track who's logged in so the screen time counts for the user, not the device?

Final note: Our WiFi is with Amazon eero which comes with some built in parental controls. I currently only use this for content filtering. Also, not all screen activity requires internet, so just controlling internet access would not be adequate.