Current Syrian government (correctly) blames Iran for propping up Assad. Iranian proxy Hezbollah had fighters on the front lines and prominent in the rape squads assaulting rebel civilian areas. Syrian govenment thus very much does not like Hezbollah and has expelled them from the country. Syria has been virtually shut down for weapons, supplies, and money from Iran. (There is still supply happening via Iraq and blackmarket dealings at the border, but this is a trickle of what used to come in via ports and air)
Current Syrian government is being extremely chill, like worrisome levels of chill, with local governments including Lebanon and The Zionist Entity, including completely shrugging off Jew actions like expanding their territory in Golan including a very strategic area, and air strikes on strategic weapons after Assad's fall as well as more recent strikes supporting Druze in internal ethnic clashes; like literally their response being "Oh well, Jews gonna Jew. We asked them not to do that and we'll raise objections in the UN. Anyway, Syria is open for business."
New Syria, especially if given international support and at the request of the Lebanonese central government, would actually be a reasonable choice for Hezbollah suppression & cleaning to all parties except the terrorists (and also the Syrians (read: Turkey)). They are arab and muslim, they hate Hezbollah, and are maintaining relations with the Zionist Entity and not threatening to exterminate jews on the daily. So no ethnic jewshine beefs as they remove kabob.