What is the protonated form of HA at equilibrium?

The term "protonated form" is misused here. Protonation means addition of proton (H⁺), and thus the protonated form of HA is H₂A⁺. This happens when a weak acid is protonated by a concentrated strong acid. For example, acetic acid CH₃COOH is protonated in concentrated sulfuric acid, and the protonated form is CH₃COOH₂⁺.

Consider the ionization of weak acid HA: HA(aq) ⇌ H⁺(aq) + A⁻(aq)
We often refer HA as acid molecule, and refer A⁻ as anion or the conjugate base of HA.
In the above equilibrium, the major form of the weak acid is HA molecule.

When the question asks about the protonated or unprotonated form,

HA is the protonated form, and A- is the unprotonated form in the equilibrium:HA <--> H+ + A-

In a solution of HA, because it is a weak acid, most of the molecules are in the protonated form HA.