RMS Titanic Binary Logistic Case Study

I have a basic question regarding clustered data:

If we fit a blrm() model on clustered data using cluster(). (e.g., repeated measurements and we think they are exchangeable), and use the predict from from rms/rmsb, it sets the random intercept to 0. Am I right that these are then predictions for a typical observation? When the prediction model will be used for a new patient, I assume we should integrate out the random effect? If we create calibration plots, should these then also use predictions where we integrated out the random effects?

Here the authors just set the random effects to 0 because they were tiny, but if they are not, what would the recommended approach? MC integration would obviously work, but that would takes a long time…