  We give an explicit finite-dimensional model for the derived moduli stack of
flat connections on $\mathbb{C}^k$ with logarithmic singularities along a
weighted homogeneous Saito free divisor. We investigate in detail the case of
plane curves of the form $x^p = y^q$ and relate the moduli spaces to the
Grothendieck-Springer resolution. We also discuss the shifted Poisson geometry
of these moduli spaces. Namely, we conjecture that the map restricting a
logarithmic connection to the complement of the divisor admits a shifted
coisotropic structure and we construct a shifted Poisson structure on the
formal neighborhood of a canonical connection in the case of plane curves $x^p
= y^q$.
