I am asking if congressional-executive agreements have an exception in the rules.
Generally, no, not currently.
(“Fast track” authority for trade agreements includes, IIRC about the procedures associated with it, an exception for a specific subset of such agreements, but applies to agreements under guidelines and priorities set by Congress, which this agreement would not.)
...and Manchin and Sinema will oppose any changes or exceptions to filibuster rules for it despite (or because of) all that, so it won't happen.