I haven't researched this (I don't have kids), but out of curiosity, what type of mobile device is your daughter using? Also, I think PiHole is a solid recommendation like others recommend.
Otherwise, from a quick Google, I don't know of anything that can integrate both Linux PC and mobile phone screen time. Honestly, this sounds like a fun project I could implement someday if I ever had the will. However, for right now, in terms of screen time all I can think of is reading system logs (perhaps via SSH) to manually analyze your daughter's screen time.
I like CoreCtrl. I don’t know how well it works with Intel and Nvidia, but it’s great on my AMD Thinkpad and desktop.
Nice thing is it’s in most distros’ repos these days.