The Haste spell states that you can
take the Attack (one weapon attack only), Dash, Disengage, Hide, or Use an Object action.
But we know that "weapon attacks" and "melee weapon attacks" are different, since weapon attacks require the use of an actual weapon, while unarmed strikes are classified as melee weapon attacks, and cannot use things like Booming Blade or Thunderous Smite as you don't have a physical weapon.
Since it says "only", does that disqualify a hasted character from using an Unarmed Strike as an attack (as it's not a weapon attack)? Or does it allow the character to instead make the usual number of attacks they can make if they use an Unarmed Strike (because of the same reasoning)?