Are my posterior predictive samples biased if I observe Y?

You should be able to use the y samples you get from sample_posterior_predictive directly. The main difference is that now you don’t get a point estimate but the whole distribution for them. You could take the mean/median to get a singe point distribution, what do you need the predictions for?

I also don’t understand what you mean by unbiased so I can’t help or give any opinion on that. Could you give some definition or reference about what you mean?

As per loo, you can use it to compare models or get weights in order to perform model averaging, but not to get predictions, the predictions come from the posterior predictive and loo is kind of using them to estimate the predictive accuracy of your model.