COVID vaccines do indeed prevent transmission of the SARS-CoV-2 virus.
Vaccine Fact Check
While COVID tests aren’t perfect, and may sometimes give false negative or false positive results, don’t believe the people pushing the idea that COVID tests can never be trusted.
Mainstream physician groups support universal face masks for school children, with the AAPS being an outlier who thinks masks are dangerous.
It is large groups of unvaccinated people in which SARS-CoV-2 continues to spread, allowing it to mutate, that is responsible for the variants we are seeing.