What does the PEGI rating of the game have to do with anything? And no it's not a public chat, it's a 5 way live chat and any recording of a child without the consent of it's guardians is not legal, at least where I live, so stop looking for excuses. Hell, you are not allowed to record without consent even adults, a TOS does not circumvent all laws and obligations.
You are confusing live chat with a recording, two entirely different things. A recording of a child in the wrong hands can have dire consequences. Unlike other shooters Valorant does allow children to play.
The only solution I see would be a system that uses AI and does not leave behind accessible records by humans.