The problem here is that the phrasing "can make on its turn" does carry the limitation of only on the turn.
It CAN ON THE TURN does mean it can not when it's not the turn.
( I can buy the book on the day I get my paycheck.)
Unlimited use of multiattack would be "can make multiple attacks" without the added qualifier.
I misread that at first, too, but I'd say we have another rogue bonus action situation going on here where two features that work exactly the same (multi attack to extra) have slightly differing wording.
It's sadly a very common occurrence in D5, where you wonder why they rephrased something, if there's an actual mechanical difference and the answer is: No, they just suck at consistent wording.
I'd say, because extra attack modifies the basic attack action in a new way when you level up, so they wanted to stress the changes and limitations to the normal attack action, while multiattack is presented as a monster feature you just use.
Also, see above.