Who's misdirecting?
The Senate has long waited until
after negotiations were completed and a bill was presented to them
before they got so deeply involved in the
treaty ratification process. Whether you or anyone else would characterize the end result of such negotiations as a treaty or an executive agreement, the ratification process is still the same. Furthermore, the Senate would still be afforded the opportunity to weight in on the bill through the normal governing process. That is why I firmly believe these 47 Republican Senators over stepped their bounds here. Yes, the process they laid out in their letter was correct from a constitutional point of view, as far as the separation of power, tenure and nullification process is concerned, but that still does not mean that these Senators get to interfere with ongoing negotiations in an obvious attempt to undermine a sitting President.
Why did senators go around the president on Iran?
Moreover, the Iranian Foreign Minister, Mohammad Javad Zarif, has already called out these 47 Republican Senators for both their attempt to undermine negotiations and in their apparent lack of understanding how international law works.
Iran Calls GOP Letter 'Propaganda Ploy,' Offers To 'Enlighten' Authors : The Two-Way : NPR
But bringing the matter back down to the domestic, yes, the Senate does have a place in these negotiations. It is "advised" if not directly then indirectly through various Senate Committees, i.e. the Senate Armed Services Committee, Senate Committee on Foreign Relations and the Senate Committee on Homeland Security, where each committee is allowed to provide their input. Notwithstanding the roles of each aforementioned Senate Committees, it is not until after negotiations have been hammered out and the framework of such is presented to the full Senate that their "consent" is required and even then the Senate can make changes to the bill via the amendment process before passage.