It seems that the phone agent was correct:
https://en.m.wikipedia.org/wiki/Soli...rance)#Details
Basically the tax is a charity-tax, and is 4.51 euro for economy and 45.07 euro for business. However these fees are, according to Wikipedia, only for destinations
outside the European Economic Area. Within the EEA the fees are about a quarter of that - which equal the fees you found on ITA.
So it seems to be related to your final destination, TLV. Even though you fly via Cyrpus (which is part of the EEA), the final destination is what counts. And in your case that is an airport outside of the EEA and therefore boils down to the highest category of fees
