I am very skeptical that chromatic aberration can be applied before a demosaic and then the result can be stored in a Bayer array again. There seems to be no advantage in storing the result of chromatic aberration correction in a raw Bayer array, which has less information, than a full array with the three RGB values per pixel. Perhaps I am not understanding it correctly?

It's not stored. It's applied to the raw Bayer data, every time, before demosaicing. Same with noise reduction.

What you can store, is metadata that informs these "first step" filters, like lens data, and maybe other sensor readings.

One of the advantages to proprietary data storage, is that you can have company-proprietary filters, that produce a "signature" effect. Third-party filters may get close to it (and may actually get "better" results), but it won't be the same, and won't look like what you see in the viewfinder.