Technically you are right but that’s small piece of the bigger picture
US wants to overtake russians in the european energy sector but they know that their gas is simply too expensive and they will never be able to take on russian gas alone but eastmed gas is something like God given gift for americans to finally achieve their dream and break Russia’s backbone(its gas exports)
Everything what happens in Syria(and Iraq) is closely connected to eastmed(and Libya)
US backed the unholy trio(Greece greek cyprus and Israel later Egypt joined) until I would say late 2019 or early 2020 but the pandemic and turkish successful intervention in Libya changed the equation in the eyes of americans and I would say israelis
The real reason why Israel and US backed greeks side in the eastmed is because that it was perfectly interlinked with their efforts in Syria to create kurdish terror state but subsequent turkish aggressive moves which were triggered by their arrogant actions destroyed american plan A and now american plan B is to work with turks and achieve their objectives regarding Russia and Iran
If they want to kickstart gas production in eastmed they need Turkey as it is very big market which will soon overtake Germany and become the biggest in Europe
@GlobalMillitary96 is right when he says that Israelis fear Turkey’s rise of a regional superpower but they are forced to work with turks if they want to sell their gas and get more EEZ from greek cyprus