RAW photo's lose original color profile after import

S-Log is primarily a video profile that is used in-camera during the processing. N.B., video is processed output like jpeg, unless you have one of the few (and expensive) cameras that will output raw video. Most Sony cameras will allow you also to use it in still jpg processing. Its purpose in both cases is to minimize data loss during that processing by creating a flat image that is unattractive but good for further editing/color grading. IOW, its sole purpose is to be an intermediate and temporary stage in the life of a jpg. Not as good as a Raw, but better than a fully processed jpg in regard to available data. As such it makes no sense to apply it in LR since the Raw is already a flat container for all the capture data. After applying S-Log or Canon’s C-log or a similar flat profile the next step would be to edit it away.

Raw images do not have a color profile. The camera can write profile information in the EXIF data, but that is all. The raw data do not change. A color profile is only applied at the moment the raw image is converted to RGB. Lightroom does not have SLOG-2 as a profile for photos, so that is why 'applying' it in the camera won't work. You will have to use a Lightroom profile that does the same thing, or make your own profile via Camera Raw.

Since you are dealing with new cameras, check the settings used by the Import dialog.

Also check the camera profile that is being applied to the images. The default is "adobe standard". You are probably looking for "camera neutral". The way I get around this is to apply an import preset selected in the Import dialog where the preset contains the settings for "camera neutral".