  We measure power spectrum response functions in the presence of baryonic
physical processes using separate universe simulations with the IllustrisTNG
galaxy formation model. The response functions describe how the small-scale
power spectrum reacts to long-wavelength perturbations and they can be
efficiently measured with the separate universe technique by absorbing the
effects of the long modes into a modified cosmology. Specifically, we focus on
the total first-order matter power spectrum response to an isotropic density
fluctuation $R_1(k,z)$, which is fully determined by the logarithmic derivative
of the nonlinear matter power spectrum ${\rm dln}P_m(k,z)/{\rm dln}k$ and the
growth-only response function $G_1(k,z)$. We find that $G_1(k,z)$ is not
affected by the baryonic physical processes in the simulations at redshifts $z
< 3$ and on all scales probed ($k \lesssim 15h/{\rm Mpc}$, i.e. length scales
$\gtrsim 0.4 {\rm Mpc}/h$). In practice, this implies that the power spectrum
fully specifies the baryonic dependence of its response function. Assuming an
idealized lensing survey setup, we evaluate numerically the baryonic impact on
the squeezed-lensing bispectrum and the lensing super-sample power spectrum
covariance, which are given in terms of responses. Our results show that these
higher-order lensing statistics can display varying levels of sensitivity to
baryonic effects compared to the power spectrum, with the squeezed-bispectrum
being the least sensitive. We also show that ignoring baryonic effects on
lensing covariances slightly overestimates the error budget (and is therefore
conservative from the point of view of parameter error bars) and likely has
negligible impact on parameter biases in inference analyses.
