Which doesn’t make much sense in the context of future Trek series. The fact that Michelle Yeoh will be starring in a Section 31 series soon, it stands to reason that the organization is still in existence even after Control was destroyed. That would mean that the mission that Kirk and Spock were given makes no sense. Why, as you say, have Starfleet clearly violate a treaty and Kirk risk his career to steal a cloaking device when Section 31 operatives could have done it without implicating the Federation? The reason: because the concept of Section 31 didn’t exist when TOS was being made. This kind of thing is why retcons almost never work in the larger scheme of overall continuity.
Have you forgotten the whole 'Kirk is Crazy' subterfuge that was going on during that episode?
(we don't really know if Section-31 was involved either way)
Kinda like "Mission Impossible" where the Fed's can claim that it was a rogue captain if the Enterprise should fail.
Of course, since the mission succeeded, as far as the Romulans know, it was still Kirk being a 'Mad King' incident.
I'm sure the Romulans sent a representative to speak to the Federation Council to demand Kirk's head.
(just like the Klingon's did in The Voyage Home)