ROCm is basically AMD’s GPU compute system, like CUDA but worse but better because the card is actually usable for desktop stuff.
However, they only support it on specific distros, and they’re really weird about what cards they support. This should be changing soon - Debian’s been working on packaging it natively, and I think so has Fedora.
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.