The governor is without power to halt payment of legislative salaries. The state constitution grants him little authority over the legislative branch, and none in this area. (And rightly so - if a governor who disagreed with the legislature's political positions or leadership had the power to cut legislators' salaries to keep them in line, it would be a gross violation of the separation of powers.) The courts might disagree, but it won't be because of the law. If the courts side with the governor, their reasoning will be rooted in short-sighted political payback for the legislature's continued denial of judicial pay raises, not legal reasoning. If the governor keeps beating on the wage drum, the senate could introduce legislation cutting his salary for errant behavior, something they most likely have the power to do.
While I am not sure a court would hear the case, the Senate is probably correct to say the Governor cannot call only the Senate back into session. While the Constitution seems to provide for that, its aim is to allow the governor to call the Senate back into session for things only the Senate can do, such as confirming appointments. The problem is that the Assembly has no interest in being called back to Albany and the Governor knows this, so he is trying to apply the provision for calling the Senate alone more broadly.
The bills enacted in the Senate last week will probably have to be enacted again to make sure they are identical to the ones past by the Assembly and to make sure the processes comply with the N.Y. Constitution's requirements. Even the Governor's Counsel has raised questions about the legality of these bills, and opponents of legislation passed during extraordinary session are sure to bring the issue to court.
My prediction based on my six years as counsel to the minority and many years thereafter studying legislatures is that the Senate will figure some way to pause their very real and important struggle over political power (which directly affects policies) to address the "must-pass" bills before them. Maybe they will even enact some rules reform along the way.