It's a fairly straightforward question.
A creature has a Multiattack option, and it also can cast the Haste spell. While under the effect of Haste, can it use the second Action to take another Multiattack Action?
My main concern is the clause of the Haste spell that limits the number of attacks made from taking the Attack Action. This is a different Action, though.
Then there is the concern of being able to use Multiattack at all, because Haste says what kinds of Actions you can take.
As you have mentioned, the spell haste tells you exactly what you may do with the extra action granted by it. The relevant portion is:
Th[e extra] action [from haste] can be used only to take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.
As the Multiattack action is a separate type of action (see the listing on page 11 of the Monster Manual, noting it is separated from ordinary ranged or weapon attacks), you cannot use it via the extra action granted by haste.
