For the purposes of the fighter Battle Master archetype, whenever a maneuver calls for a "weapon attack" does that include an unarmed strike?
Yes, an unarmed strike is a melee weapon attack. From the official Sage Advice Compendium on page 10, under What does “melee weapon attack” mean: a melee attack with a weapon or an attack with a melee weapon?:
For example, an unarmed strike counts as a melee weapon attack, even though the attacker’s body isn’t considered a weapon.
As another answer points out, the revised wording from the errata is a little ambiguous. Fortunately, we have the official clarification above, which leaves no room for uncertainty.
No, unarmed strikes aren't considered weapons. An official erratum has stated that
Weapons (p. 149). Unarmed strike doesn’t belong on the Weapons table.
...[The melee attack errata] lets melee weapon attacks use unarmed strikes, despite those strikes not being weapons.
So when using a Melee Weapon Attack you can replace the required weapon with an Unarmed Strike, including for the purposes of this class feature.
From the Errata:
Melee Attacks (p. 195). The rule on unarmed strikes should read as follows: “Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.”
The wording on this is a bit strange.
You could interpret it to be saying that instead of making a melee weapon attack, you can make an unarmed strike (inferring unarmed strikes are distinct from melee weapon attacks).
Or, you could interpret it to be that instead of making a melee weapon attack with a weapon, you can make one with an unarmed strike. This interpretation is a bit confusing, since it implies that your fists are not weapons, yet are capable of making weapon attacks.
You could make a case for either interpretation - the former plainly makes more sense as written, but the latter might be their attempt at enabling you to use your fists the way you would weapons for certain attack mechanics, while still not allowing you to do something silly like parry a hammer-blow with your skull, or enchant your feet to do +1 damage.
The errata states that you can use an unarmed strike in place of a weapon when making a melee weapon attack. Your unarmed strikes are still not considered melee weapons. Based on the wording of certain maneuvers like Disarming Attack, they require a weapon attack (not to be confused with a melee weapon attack), with an actual weapon to activate.
Disarming Attack: "When you hit a creature with a weapon attack"