I'm curious why you think Trump's approach to Israel is more important to Saudi Arabia than his approach to Iran. I would think that Iran is actually a bigger issue for the Saudis than Israel. It certainly affects them a lot more. And I expect they probably will like Trump's approach to Iran better than Biden's.
I hadn't actually made that point, but, as you bring it up: it Trump's approach to Israel is more important than his approach to Iran, to the Saudis. This is because the US has largely been sidelined on this issue. China has brokered a deal between Saudi Arabia and Iran, in which the two reestablished diplomatic relations. The second round of these talks was quite recent:
The constant American flip-flopping on Iran has, I believe, exasperated the Saudis, and the Arab states in general. They have come to see the US as an unreliable ally. Biden's weakness (perceived or otherwise) in relation to Israel has just furthered this perception. China saw this as an opportunity, and deftly stepped into the breach.
Saudi now has a more stable relationship with Iran, which benefits them. Sure, there may be an element of window-dressing- they are never going to be friends- but this agreement does add some stability to the situation, which the ever-changing American approach never got close to establishing.
Israel is
the hot topic in the Saudi press right now. The effects on Saudi Arabia, and the region in general, are far wider and deeper than what's now happening with Iran. The Saudis fear a regional war- as does Iran. Israel, or to be more precise, Netanyahu, doesn't. In fact, he needs one, to maintain power in Israel. As long as America is backing him, he can do what he likes, with impunity. If Trump gives him unconditional support, then Netanyahu will have a free hand to continue to attack who he likes, in whatever way he likes. This will further inflame Muslim public opinion, not just in the Middle East, but around the world. The Saudis want to keep their position of control and dominance over Islam, or at least Sunni Islam. If Muslims on their doorstep are being bombed and starved by Israel, that makes it difficult for the Saudis to do that. Furthermore, there will be no accord between Saudi and Israel as long as these wars continue. This accord is something the Saudis want. MBS wants to end his country's pariah status, and an agreement with Israel would really help that.
So, yeah, how Trump deals with Israel does, in my opinion, matter more to the Saudis than what he does with Iran.