Edit: Corrected to sentence about imputation of outcome values.
No worries.
The key problem here is not so much what brms can do out of the box (I do get it into brms, it just involves a few additional lines of code). The key problem is that if one estimates (1) regression coefficients and (2) covariance of outcomes with predictors and an auxiliary variables, these two things interfere with each other (see details here). Maybe you have an idea why this is happening?
About the scope of brms: I think it would be great if brms had some facility to deal with missing outcome variables would allow to condition imputed outcome values on auxiliary variables, i.e. variables that are not part of the regression model. The reason is that if one does a complete case analysis when only predictor values are missing, the only effect will be that the variance of the regression weights will be overestimates. That’s not nice, but it’s not so bad either. However, if outcome values are missing systematically, the situation is much worse because the expectation of the regression weights will be biased.