This is not valid, as m and T are not defined. It would be good to use the new array syntax which is more clear (and the old syntax will go away)
array[T] vector[m] y;
_lpdf functions return sum of log densities
No, vectorization is not possible (at the moment), and a loop like you suggested is needed to get T terms.
For timeseries model, you may also be interested to look at Approximate leave-future-out cross-validation for Bayesian time series models • loo. In case of time series, LOO is also valid for certain purposes, e.g. focus in the conditional observation model, or task is to impute single missing values.