What do you mean by regional war?
Egypt will stay out, Jordan will stay out and crackdown on its Palestinians, Iraq will send troops to the Syrian border to keep their civilians out, Iran isn’t ready for a fight yet and will just shout a lot.
Syria’s problem is that they have one client they can’t control and no friends. Everyone knows where those missiles came from so other then some loud talking (if that) no one is going to help Syria fight Israel.
I would think a war that involved Israel, Hezbollah, Syria and Lebanon would qualify as a “regional war”.
2 other potential combatants are Iran and Hamas. A few of Iran’s military options include 1) attempt to close the Strait of Hormuz 2) fire ballastic missiles at it’s Gulf neighbors either of which could pull in further combatants . . . the risk of a regional war is real IMO