I have run [insight](insight::get_variance) on a fitted glmmTMB model with a "compois" (Conway-Maxwell Poisson) family:

richness_glmmTMB<- glmmTMB(richness ~ vl100m_cs + build50m_cs_o + roads100m_cs + (1 | site/neighbourhood), data = df_Bird, family = "compois", na.action = "na.fail", REML = F)
var.distribution is returned as the Dispersion parameter for the Conway-Maxwell (from glmmTMB summary):

Dispersion parameter for compois family (): 0.473

Does this represent an accurate approximation for Distribution-specific variance for a Conway-Maxwell Poisson (compois)? Could Conway-Maxwell be a candidate for additional model support in "insight".

Thank you very much for your time and consideration.