Our knowledge is not that precise yet.
What we do know, based on models, is that "silent" transmission accounts for about 50% of covid-19 infections.
https://abcnews.go.com/Health/asymptomatic-presymptomatic-pe...
But the ol' maxim applies here: absence of evidence is not evidence of absence
That applies to infection/transmission via schools in general. Precisely because we don't have decent testing and tracing, we have a large number of cases whose origin is unknown. Schools have to be considered as one possibility, especially considering the several cases where reopening schools has been strongly correlated with spikes in infections. The precise mechanism doesn't matter. It's a red herring. Whether it's kid to kid, parent to teacher, cafeteria workers, whatever, it seems to happen some of the time. Until we've clearly ruled out a cause for those unknowns, we have to consider it still operative.
"Our results indicate that silent disease transmission during the presymptomatic and asymptomatic stages are responsible for more than 50% of the overall attack rate in COVID-19 outbreaks."
And we know that, while presymptomatic spread is an issue, asymptomatic spread is between rare and nonexistent.
The fact that children tend not to be diagnosed because they tend much more strongly than adults to be asymptomatic when infected is not irrelevant to their propensity to spread the disease.