Testing Conformal Weyl Gravity with Plasma Modified Black Hole Shadows and EHT Constraints

We study the shadows of a charged rotating de Sitter solution in fourth order conformal Weyl gravity (CWG) immersed in plasma and analyze the joint charge-plasma constraints. Our main goal is to distinguish observational effects caused by the dispersive plasma environment from those caused by the underlying gravitational theory. Within a separable Hamilton-Jacobi plasma model, we derive the radial and angular photon potentials, the equatorial finite-distance deflection angle, and the finite-observer shadow boundary due to the asymptotically non-flat nature of the CWG spacetime. Our results separate two effects. Increasing the plasma strength generally reduces the shadow radius, the signed deflection angle, and the energy emission peak in both CWG and GR. Charge ($q$) produces a stronger theory dependence: for the representative parameters studied, increasing $q$ enlarges the CWG shadow but reduces the GR shadow. The lensing behavior independently supports the geometry-dependent response found from the photon region and shadow observables. We further compare the finite observer dimensionless shadow radius with EHT-inferred size intervals for Sgr~A$^*$ and M87$^*$. Our results indicate that plasma effects can mimic part of the shadow size shift, but the distinct charge response of CWG offers a potential observational route for separating conformal gravity signatures from environmental propagation effects.