Europe (and other countries worldwide) seems to be in a starting phase of the new wave. To be honest, I am myself puzzled by the severity of the outbreak in some European countries; perhaps less in others.
So why suddenly are we seeing rapid growth in cases when we already thought the pandemic is over?
I can think of a range of reasons. A relatively low vaccine coverage or use of lower efficacy vaccines, vaccine efficacy waning, behavioural changes (abandoning all restrictions), winter (bringing people inside).
It is possible that we will not have a single explanation for all these countries and we might indeed be seeing different epidemics (i.e. driven by different factors) which we interpret as the same wave.
We might also be seeing countries at different stages of the outbreak, some (Bulgaria?) already being past the “fourth wave”, some having entered it in September (Austria, Poland), October (Denmark), some entering now (Germany, France, Portugal), and perhaps some that will either enter it later (USA), or never (Israel?).
It is also possible that Israel already had its “fourth wave” and thanks to its “burning out” effect and a rapid third vaccination campaign, managed to stop it.
So, what we are looking at in Europe now is Israel’s August-September wave shifted to November and perhaps magnified by other factors like lower overall vaccination and much lower restrictions.
The UK seems to be standing out, by having a rather steady, high level of epidemic cases. Again, possibly a combination of factors, including little effort in preventing spread in schools, a large proportion of AZ vaccines, no masks (in England).