set times propagation

Hi,
There is something not entirely clear in how time is managed:
if i set the times to a recording object with recording.set_times(correct_times) and I sort that object the sorting object will not have the correct_times, so I have to do again

recording.set_times(correct_times)
sorting.register_recording(recording)

I find this quite unintuitive, is there an internal reason for this to be necessary?
For example I cannot create a sorting analyzer directly with this:
create_sorting_analyzer(sorting = read_sorter_folder(f"{path_recording_folder}/spike_interface_output/probe{group}"), recording=raw_rec.split_by(property="group")[group], **job_kwargs)
because I always have to load the sorter first and register the times.

Thanks!!

Start by tracing recording.set_times(correct_times), sorting.register_recording(recording), and create_sorting_analyzer through the recording and sorting object flow. Determine where times are stored or lost when a recording is sorted or loaded from a sorter folder. Done should mean the documented analyzer workflow preserves the intended times without requiring a second registration step, with coverage for the example in the issue.