I agree that Syria is already laden with plenty on their plate but that is not really a factor in this equation. If anything it is beneficial to other players against the Israeli state.Syria has enough troubles. It is barely a state.
As a country they (Syria) have very little say in their own fate or the fate of the region.Why would they want to be dragged into a conflict with Israel?
Anything tangible that Syria appears to bring to the fight is actually via others that are using Syrian territory and tribes in a proxy war against Israel and the West. Exactly the same as the West using Ukraine as a proxy to execute actions against Russia.
Most of the Syrian people just wish for a moment of normalcy, the same as most of the citizens of Ukraine. As with most of the world, Syria and Ukraine are being used as a means to an end by a very small group of people.