Does an attack granted by Haste trigger two-weapon fighting?

Question

I'm a level 6 Bladesinger Wizard. I have Haste cast on myself. I am wielding two shortswords. If I use my action to Cast a Spell, such as Booming Blade, and use my additional action granted by Haste to Attack, can I use the bonus action attack granted by two-weapon fighting?

I have considerations on either side. Two-weapon fighting requires you to take an Attack action. It seems that Haste grants an Attack action, but it is modified and limited, and those limits may extend to two-weapon fighting as well.

Answer 1

Yes

Two-Weapon Fighting
When you take the Attack action [...]
(PHB, p. 195)

Haste
The target [...] gains an additional action on each of its turns. That action can be used only to take the Attack [...] action.
(PHB, p. 250)

This is pretty straight-forward. Haste doesn't grant you an additional attack, but a real action, which you can use to do one of the mentioned things, including taking the Attack action. The fact that it is limited doesn't change that it would be a real Attack action. Two-Weapon Fighting is triggered by taking the Attack action, so this works. Also, the extra attack from Two-Weapon Fighting happens as part of your Bonus action, so the limitation to 1 (one) attack during the action granted by Haste doesn't apply to that.

Of course, the usual caveats apply; You need two different weapons, both weapons must be light unless you got the feat, and you can't have used your Bonus action already.