What is the most appropriate approach to compute an ICC for a brms MLM?

Dear Stan community,
I need to compute a multi-level model, using the package brms. I would like to compute an ICC for my data. This issue has previously been discussed in this post Brms: How to get the ICC or VPC value for a multi-level negative binomial model?
and as recommended there, I have used


to compute the variance ratio.

Previously, I have attempted to ‘manually’ compute the ICC, using the following steps:

variance_components <- VarCorr(fit)

# Extracting the variance component for participants
variance_participants <- variance_components$participant.$sd["Intercept", "Estimate"]

residuals_model <- residuals(fit)
residual_variance_manual <- var(residuals_model)

icc <- variance_participants / (variance_participants + residual_variance_manual)

This has resulted in a very high ICC of 0.8.
Now, when using performance::variance_decomposition(fit), the variance ratio comes out at 0.05, with CI 95% = [0.00, 0.11].
I’m not quite sure what to make of this. Is my manual computation of the ICC so far off?
I appreciate any advice on this!

Best wishes,