Can someone clarify the positions of the main Haredi groups/communities in the diaspora on the State of Israel?

I must admit that I’m a little confused.

I know Satmar are anti-Zionist based on their understanding of the Three Oaths, and their belief is detailed in the book “Vayoel Moshe”. However, I also heard that they wouldn’t support anything that may put the lives of the millions of Jews in Israel in danger, and unlike Neturei Karta (who are one community within haEdah haCharedit in Jerualem, right?) , they don’t ally themselves with the Palestinian cause. Idk understand what they want from Jews in Israel – do they want them to establish a binational state with Palestinians, so that it wouldn’t be a Jewish state and therefore there wouldn’t be a halachic problem in that from their perspective? Is it correct to assume that if a war breaks out between Israel and another country/paramilitary group, they would daven for the safety of Israeli Jews? I read somewhere it happened during the Yom Kippur War.

As for Agudath Israel – I assume they don’t call themselves Zionists. Is it because of the Three Oaths as well, or a general rejection of the secular background of Zionism? It’s my understanding from a previous post here that most Haredi shuls don’t daven HaNoten Teshua for Israel, and don’t recite Hallel on Israel Independence Day, but I remember a commenter pointing out that Chabad shuls daven for the IDF. Furthermore, Agudath Israel participates in the Israeli elections and its representatives are members of the new Israeli government. Also, in Siyum HaShas 2020, they showed RZ IDF soldiers on the screen.

What about Litvak communities? Most Litvaks in Israel vote, and the Litvak Degel HaTorah runs together with Agudath Israel for the Israeli elections. Do most Litvaks in the diaspora approve of it?

Finally, are there sometimes differences between the official positions formulated by the Gdoilim and the sentiments of the communities? I know that in Israel some Haredi youth is blurring the lines between Haredi and Religious-Zionist identities (some youth sympathize with the Hilltop Youth, or show support for Ben-Gvir), and Yated Ne’eman even warned readers against fangirling over a Prime Minister. I also remember watching YouTube videos where Muslim YouTubers tried to get people from Hassidic communities in the US and UK to speak against Israel on camera (for example during Operation Guardian of the Walls), and they were given the cold shoulder.

So, can someone provide a Bi’ur of the issue of Haredim in the diaspora and Israel?