My question is, is the 𝑆 according to Boltzmann an entropy change as well?

No -- Boltmann gives a value to the entropy, not just the change in entropy.

Even in pure thermodynamics, (ie, using Clausius's definition), the third law of thermodynamics also fixes the absolute value of the entropy. The third law says that the entropy must approach a constant at zero temperature, where teh constant is given by Boltmann's constant times the natural log of the number of degenerate ground states of the system.

My question is, is the 𝑆 according to Boltzmann an entropy change as well?

No -- Boltzmann gives a value to the entropy, not just the change in entropy.

Even in pure thermodynamics, (i.e., using Clausius's definition), the third law of thermodynamics also fixes the absolute value of the entropy. The third law says that the entropy must approach a constant at zero temperature, where the constant is given by Boltzmann's constant times the natural log of the number of degenerate ground states of the system.