Like modern Syria. The SSNP was heavily influenced by European fascism (look at
their flag), and was generally popular among non-Sunni Arab elements of the populace. Its founders were Christian-but then again, the Baath party was founded by a Christian too, and only later became dominated by Alawites. The SSNP was also founded in Beirut, so you might see some more Syrian irredentism towards Lebanon-but then again, there was a heck of a lot of that IOTL, with Syria
refusing to send an ambassador to Lebanon until a few years ago because they didn't recognize its existence. And yes, a SSNP Syria wouldn't exactly have a good relationship with Israel-which, again, makes it no different from the Baath party.