Literally none of the evidence on the website's own "Why" page supports their suggestion: https://www.waituntil8th.org/why-wait
All of the studies (bonus points for linking to news articles instead of directly to the studies) have something to do with "time spent using screens/a phone/social media", but nothing to do with age of first use.
How can anyone trust this website has any basis in reality when they wrote a whole page explaining why and none of it was applicable?
Of course parents should regulate how much time their kids spend on electronics (similar to how parents of previous generations would prevent kids from watching TV 5 hours a day) - but this website presents no evidence that giving a kid a smartphone in 8th grade rather than 5th grade would make a meaningful difference.