Yes, the inverse square law applies to Type Ia supernovae when we define luminosity distance. Their observed flux is related to intrinsic luminosity by:

F = L / (4 * π * D_L²). But in an expanding universe, one must also account for Redshift Effects. The luminosity distance includes both geometric spreading and redshift/time dilation which leads to: D_L(z) = (1 + z)² * D_A(z). This relation comes from the Etherington reciprocity theorem, assuming photon number conservation and a transparent universe.

Reference:

Hogg, D. W. (1999). (Distance measures in cosmology)

Amrit Roy.

Thank you for the helpful reference. Luminosity distance at section 7 of the article.

Hogg, D. W. (1999). (Distance measures in cosmology)

https://arxiv.org/pdf/astro-ph/9905116

Glad to be of help! Keep posting such questions, people do learn several things in the middle, in order to answer such questions.