This freshly announced mutual recognition follows the one between the UAE and Israel, which set a new pattern, with Bahrain and possibly others (Oman?) predicted to follow. I am not surprised it was Bahrain that was next, although it may prove to be the only one. There are several reasons why it was most likely to be next, and why we might not see Oman join in, although that cannot be ruled out.
I see three reasons why Bahrain was most likely to be next, although there are really two fundamental ones with the third arising from those. The most fundamental one is that of the 6 members of the Gulf Cooperation Council (GCC), now largely in shatters due to the sanctions on one of them (Qatar) by several others (Saudi Arabia (KSA), UAE, and Bahrain), is the only one where a Sunni minority is ruling over a Shia majority, with the Sunni-Shia conflict a central part of the conflict with Iran that many of them have, with Iran run by Shia, of course, where they are a majority. The Shia of Bahrain have been restive and rose up against King Hamad during the Arab Spring that began in 2011, only to be violently put down. But, unsurprisingly, the king and those around him are especially worried about the Shia and have strongly supported the anti-Iran coalition, which includes Israel. It is this alliance that is at the heart of the new round of recognitions, with UAE leader, Prince Zayed, arguably the leader of the anti-Iran group in the GCC, along with KSA Crown Prince, MbS, although due to opposition of the Saudi religious leaders who are concerned about the Palesrtinians, MbS himself is not seen as likely to follow UAE and Bahrain to recognize Israel, although there is clearly a de facto alliance against Iran between them.
A second reason Bahrain was more likely to be next is that it is more subject to US pressure as it hosts the home base in the Persian Gulf of the US Navy's 5th fleets, something rarely mentioned in the media, and has been since the 1950s. That dates back to when what is now the UAE was still being ruled by UK as the Trucial States. On top of that Bahrain is the smallest of the GCC members and also is the one that has been running out of oil more than the others (all of them produce at least some oil). In short, King Hamad is much more susceptible to US pressure to recognize Israel, although given his unhappiness with his Shia population and support for the anti-Iran coalition, he has been more inclined to go along anyway.
Another reason, which basically follows these others, is that Bahrain is indeed part of the GCC group that is sanctioning/boycotting fellow GCC member, Qatar, for its apparent unwillingness to join the anti-Iran coalition. Indeed, Qatar and Iran have a joint deal for managing certain natural gas fields in the Gulf, and Qatar, which has the world's highest per capita income, also hosts al=Jazeera, which has reported on dissident movements in several of its GCC partners, another source of anger. Of course, while Trump initially forgot about this as MbS and Jared Kushner pushed him into supporting the anti-Qatar sanctions, Qatar hosts a major US air base, so the US military did manage to get to Trump to back off overtly supporting the anti-Qatar boycott, although the US has failed to bring that conflict to a conclusion.
So, what about the other two members of the GCC: Oman and Kuwait? I cannot rule out Oman recognizing Israel, but it lacks several of the elements one finds in both Bahrain and UAE. One is that it alone among Muslim nations in the world is not dominated by either Sunnis or Shia. The majority of the population and the leaders are Ibadi Muslims, an ancient sect of Islam, that is barely present anywhere else in the world. But that has allowed Oman to stand aside from the regional Sunni-Shia conflict, and indeed it has played a role as intermediary between the two sides. It was through Oman that the Obama admin made its initial approaches to Iran when it started negotiating the JCPOA nuclear deal that Trump has since withdrawn from. It is also Oman that shares with Iran the crucial Strait of Hormuz at the entrance to the Persian Gulf. As a result of this, Oman has not joined the anti-Qatar sanctions/boycott, although it is not as pro-Iran as Qatar seems to be. Oman is extremely independent and proud of being so. It joined the GCC to keep the Saudis happy, who organized the group, but it does what it wants. It indeed has apparently had informal friendly relations with Israel, which may lead it to recognize Israel as part of its being friendly with everybody policy. But it would not be doing so either as part of an anti-Iran alliance or to kowtow to the US, although it does not mind keeping the US happy as well.
As for Kuwait, it has long been at the top of per capita income among this group, having the second largest pool of oil in the world, one of the reasons Saddam Hussein invaded the place. It has been surpassed by Qatar in per capita income, but it remains very high up there and is also fairly small, although bigger than either Bahrain or Qatar. The problem for Kuwait is that it almost borders Iran, with just a small amount of Iraq between them (where the Shatt-al-Arab empties into the Gulf, the short river that is formed when the Tigris and the Euphrates come together). It is predominantly Sunni and has a long history of friendship with the Saudi royal family. But its proximity to Iran has it not wanting to join in the overtly anti-Iran alliance, in that regard being a bit like Oman. Also, it has a large Palestinian refugee population, possibly up to a quarter of the population, and recognizing Israel is not something favored by that portion of their population.
So, it is not surprising that Bahrain has recognized Israel. Oman might do so also, although I am not holding my breath on that one, and if they do, it will be to maintain their independent "friendly with all sides" approach rather than the kowtowing to UAE and US that is going on heavily with Bahrain.