I don't think Hezbollah wants to get into a regional war over this. They might intensify things in the north a bit. And as to the Houthi response, I think they're already doing all they can. They're not holding anything in reserve. They've announced US warships are targets but haven't really accomplished any dramatic actions. They've forced some companies away due to insurance carriers, yet other vessels that are for example British owned are sailing through and not caring about a few drone attacks causing small fires. They so far seem to simply lack the kind or amount of advanced weaponry to actually really put a stop to shipping by sinking a cargo ship or doing real damage to a US warship which is what is necessary for the message to sound any stronger from them and to exert any more pressure. Given their situation, years of civil war, poverty, strangled by sanctions, they're doing the best they can but I really don't think we should expect anything more than some western ships continuing to take the long way around due to their insurance carriers forcing them to while others continue to go through anyways and indeed dock at Israel.
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.