Thinking about it, the first sentence above is sophistry; the Chimaera is the flagship as long as the admiral is aboard. So that argument fails.
Nonetheless, it seems that all the New Republic knows at this point is there are rumors of an Imperial military genius -- who he is, what his rank is, the fact that he is an alien, the fact that he has made the Chimaera his flag -- all appear to be unknown at this point.
None of this changes the fact that C'baoth knows very well what it is. So if Luke reveals the attempt, he will immediate suspect Thrawn, who will claim it was an unrelated trap and they happened on Skywalker by mistake.
..
Wait a minute.
That's it
This entire charade with the freighter isn't solely for the benefit of the New Republic.
It is also for the benefit of C'baoth, should Luke succeed in escaping.
Which doesn't mean some of this isn't aimed at the NR as well. After all, exactly how does the Grand Admiral know Luke Skywalker's precise timetable and itinerary? Pretending this is an accidental encounter may put the security hounds in the Republic off the scent. For awhile , at least.
Respectfully,
Brian P.