Agreed, I think almost all the major players in the region want anything but a regional war.

The outlier is, of course, Israel. I don't think they want it, exactly, but it certainly seems that they will continue pushing and pushing, until a fire is started the US gets pulled in on- all facts on the ground seem to support it, from the (natural, in hindsight) derangement of their settler-colonial society and its "necessity" of further continuing on this genocide to the last glimpse of Palestinian dignity, self-determination, and existence within their own land is destroyed to maintain the settler apartheid state, to the political career of Bibi on the line, and the development of the global south contrasted the the diminishing of the west (and diminishing of support in the west)- I think there is no end in sight, till a larger war actually takes place.

Frankly not even the successful genocide of all Palestinians, something that is not going to happen, particularly not without expanding the war well beyond Palestine- will be able to sate Israel. The mentality is that the genocide and settler-colonialism must continue full speed, because very soon, perhaps within less than a decade, they won't be able to get away with it. Israel is the US/Canada, if they were faced by indigenism on all sides and saw their opportunity to reach the Pacific slipping away- and even that doesn't quite cover how "dire" the Zionist project is (entirely deserved, of course- a curse on all genocidal settlers). I can't see them doing anything other than escalating further and further.