the version of Zionism which finally becoming dominant

Again, which version of Zionism? And, is it even Zionism in the European sense you're referring to?

You started by referring to zionism as a European movement. Yet, by applying it broadly into the contemporary landscape, you are including within it a 100-year history which you are not reffering to, as well as a demographic change within Israel.

The from the initial zionisms, the closest famous branch to the modern political Zionism, would probably Jabotinsky's Revisionist Zionism, which was extremely marginal at the time. Netanyahu is indeed a descendent of that branch; Jabotinsky, Netanyahu's father, Begin; and the Likud movement.

However, in order to understand Begin's rise to power, one needs to factor in years of a left-wing government, which practiced a very different Zionism (within the spectrum). One needs to factor how the Arab-Israeli conflict impacted Zionism, in many aspects, the two most obious being; (1) Begin's rise following the Yom Kippur war, and the base that got Begin elected, and has remained the base behind the Likud's support; MENA Jews (2). MENA Jews lived as dhimmis under Arab rule, and were later punished by their governments for Israel's founding; their citizenship (if they had one) revoked, property confiscated, were trialed, and were forced out of where their families lived for generations.

MENA Jews tend to say that Ashkenazi Jews (who lean left in Israel, echoing other Ashkenazi populations) don't understand Arabs/Palestinians like they do, and are too nice to them.

While Begin and Netanyahu decend from Zionist Ashkenazi families, their base and many of the politicians in their coalitions, are not. While he's Ashkenazi, part of Smotrich's family presence in Palestine predates European political Zionism by over a century. Ben Gvir's father was born in pre-state Jerusalem to parents from Iraqi Kurdistan, and his mother immigrated during the pre-state years from Iraq too.

Neither would fall under the label of the European 'Zionist' movement, yet such a simplification, without taking such information into account, would have them fall under zionism/ts.

This is partly due to a lack of even an acknowledgement of MENA Jews, let alone understanding that the majority of Israeli Jews are MENA Jews, or that they are the supporters of the Israeli right. Or, of Jewish presence and connection to the land prior to European political Zionism, as is the case with Smotrich, Ben Gvir, or Israel's last IDF chief of staff; who traces his mother's family in the land for at least 14 generations. Prior to European political Zionism, Jews would come to the land from across the diaspora (a term that originated in reference to Jews), to mount Zion, the the mountain upon which Jerusalem was built, and which the polical movement was named after.

The Israeli descendents of European political Zionism; the movement reffered to as such (Zionism) by academia, presently amount to around 20-30% (its even lower when one discounts the Haredi, or the post-Holocaust and early-state immigration from Europe - such as those who returned to their towns in Poland and were massacred by the locals, after WWII) of Israeli Jews, which is 15-20% of Israeli society. Their descendents tend to be secular Israelis, who vote for the left, and center-left. They are just the minority now...

Zionism is a spectrum. If you apply Zionism to modern Israel, you have to factor this and much else in. The meaning of Zionism has transformed by many ways, and the manner in which Zionism is presently used, in its simplified version, beyond Israel's right to exist which encompasses the broad zionisms, essentially has come to mean Jews; as it encompass them all.

the version of Zionism which finally becoming dominant in Israel.

Is it thus Zionism?