Feature Request: init recording from sorting (phy, kilosort)

For a "sorting" based on read_phy / read_kilosort (class BasePhyKilosortSortingExtractor), the params.py file is read here

https://github.com/SpikeInterface/spikeinterface/blob/85f4ff3b4c35532aa5df3238e15f901d439fadc5/src/spikeinterface/extractors/phykilosortextractors.py#L60

params = read_python(str(phy_folder / "params.py"))

For the sorting, only the sampling rate is used.

It would be helpful to have this result (params dictionary) available (like self.params = params), especially for the associated recording read using read_binary (class BinaryRecordingExtractor).

Then it could be as simple as

file_path = params["dat_path"]
sampling_frequency = params["sample_rate"]
dtype = params["dtype"]
num_channels = params["n_channels_dat"]

recording = read_binary(file_path, sampling_frequency, dtype, num_channels)

We could also have a function like read_binary_from_sorting which accesses sorting.params.

And this is just one more line.

sorting_analyzer = si.create_sorting_analyzer(sorting=sorting, recording=recording)

Start in src/spikeinterface/extractors/phykilosortextractors.py at BasePhyKilosortSortingExtractor and the read_python call around line 60. Trace how read_phy, read_kilosort, and read_binary expose extractor metadata, then decide whether sorting parameters should be retained or a helper should use them. Done means the requested sorting-to-recording initialization path is available and the existing sorting behavior remains intact.