Why does adding a gain to a Sallen-key second order HPF change the amplitude response?
In all Sallen-Key filters, the opamp does not only provide gain to the input signal. It is the main purpose of the active block to allow positive feedback.
Only in this case, the circuit is able to produce a conjugate-complex pole pair - which is the precondition for allowing pole-Q values (Qp) larger than 0.5 (Remember: Qp=0.7071 for Butterworth response and Qp=0.9565 for Chebyshev with 1dB ripple).
That means: Larger gain (all other elements remain unchanged) makes more positive feedback (equal to higher Qp-values). And - there is a direct relationship between Qp and the form of the transfer function in the pole frequency region (amplitude peaking).
(Comment: The shown second circuit does NOT provide a gain value above unity).