Reprex (courtesy of https://easystats.github.io/blog/posts/performance_check_collinearity/):

library(glmmTMB); library(performance)
#note: needed to also install the insight package before installation of performance

data(Salamanders)

# create highly correlated pseudo-variable
set.seed(1)
Salamanders$cover2 <-
    Salamanders$cover * runif(n = nrow(Salamanders), min = .7, max = 1.3)

# fit mixed model with zero-inflation
model <- glmmTMB(
    count ~ spp + mined + cover + cover2 + (1 | site), 
    ziformula = ~ spp + mined, 
    family = truncated_poisson, 
    data = Salamanders
)

# now check for multicollinearity
check_collinearity(model)

The performance package offers check_collinearity function that handles ME models:

 library(performance)
 

 check_collinearity(model)
# Check for Multicollinearity
#--------------------------------------------------------
* conditional component:

Low Correlation

 Parameter  VIF Increased SE
       spp 1.07         1.04
     mined 1.17         1.08

High Correlation

 Parameter   VIF Increased SE
     cover 19.30         4.39
    cover2 19.12         4.37

* zero inflated component:

Low Correlation

 Parameter  VIF Increased SE
       spp 1.08         1.04
     mined 1.08         1.04