In case it might be helpful, in this answer I showed how to reproduce what conditional_effects is doing using tidybayes::epred_draws to extract the expected values from the posterior predictive distribution and summarize them to get the median and credible intervals.
The other thing to be aware of is that for each predictor variable in the model, conditional_effects creates a data frame of values at which to calculate the conditional effect of that predictor variable. For a numeric variable, this data frame will have 100 rows of values spanning the range of that variable. For a categorical variable, the number of rows will equal the number of categories. If there are other predictor variables in the model, they will be set to their mean if numeric or the reference category if categorical.
For example, for the regression in your initial post, you can see the data frame conditional_effects creates for X by running:
ce = conditional_effects(hurdlefit)
ce[["X"]]
ce is a list of data frames, one data frame for each of the predictor variables, and it also of course includes the median and credible intervals for each row, since conditional_effects takes care of summarizing the posterior expectations. You would need to create a similar data frame (or data frames, for multiple predictor variables) to pass to epred_draws.