Measuring $R_c$ with exclusive $c$-hadron decays at FCC-ee and an outlook to $R_s$ and $A_\text{FB}^s$

This analysis note is meant to be a telegraphic transcript of an ongoing analysis aimed at assessing the precision that can be reached at FCC-ee for the partial-width measurement of $Z \to c \bar{c}$. Intermediate results are presented with a focus on detector requirements. Furthermore, it presents the idea of measuring $R_s$ and $A_\text{FB}^s$ with exclusively reconstructed strange hadrons.