It certainly looks simplistically like total cases in the period June-December is the main dampener on omicron cases, not vaccine rates or anything - however we'd really need more of that re-infection data I think to be more confident that it's that (ie we'd see the re-infections being mostly from cases older than 6 months in the UK)
I don't really buy the BA.2 lineages question, there's no logical way it could be all over Europe except in the places where there were lots of delta cases, unless delta was peculiarly protective just against BA.2, which doesn't make sense.
The US states could also reveal some differences on this, but the problem there is the confounding that the US states that had lots of delta are quite different in their case reporting too, it being such a varied issue. So I think you might need local knowledge to tease it out.