You have the same access to the data that I do. It's just google. We know when countries re-opened their schools, we know when peaks in transmission happened, and we know when those two things didn't align. Just from two google searches per country. If you really wanted the answer to the question rather than trying to make a point, you'd be better off just googling these things for your own peace of mind. Instead it looks like you're only googling evidence that fits the narrative you want to put out there. But sure I'll pull up some numbers.
To pick up on your point about the scientific assessment from NI, I think it's worth clarifying a couple of things. They didn't say that closing schools would reduce the R rate by 0.5. They said it oould be as low as 0.2, or as high as 0.5. They gave a more confident prediction that secondary schools would a) be more likely to spread the virus, and b) be around 0.35. So if secondary schools are more likely to spread it, and their best estimate is 0.35 for them, then we can safely assume their estimate for primary schools is closer to 0.2. Very possibly lower. They also said in the same document that overall the assessment is provided with "low confidence, as unclear how much schools may contribute to community transmission." and other measures related to education are "low confidence, as remains unclear how infectious children may be." And their modelling on education settings was based on influenza, because as they said repeatedly, they haven't got any clear evidence on covid spreading in classrooms. Despite the fact that you believe it to be an obvious driver of this second wave, they can't find the evidence for it at all.
Pages 13-15
here, Geebs. The scientists aren't saying different things, they are just being misrepresented. You don't need to trust my words or his words, the advisers laid it out incredibly thoroughly there. The views from NI's expert are entirely consistent with the consensus that older teenagers in secondary school are more likely to spread it than young kids in primary school, and that there is no evidence that schools are hotbeds of transmission.