How can I tell if my Sony ILC is applying lens corrections to in-camera JPEGs?
The chances are almost certain the information you want is contained within the EXIF information embedded in the image file. If Adobe ignores the lines, usually in the maker notes section, that tells you what options were turned on and off when you shot the image, use another application to view the more complete EXIF info. IrfanView and EXIFTool are both popular free apps that will show you much more of the EXIF info contained in an image file than Adobe products will.
What EXIF fields will inform us of corrections that have been applied to the file in question? E.g., I queried a JPEG and I see things like 'Distortion Corr Params Present: Yes', and 'Distortion Correction: None'. Plus there are 'Distortion Corr Params', 'Vignetting Corr Params', 'Chromatic Aberration Corr Params' ... so it appears there are a lot of correction data present, but not applied? And is it obvious how to tell Lightroom to apply these parameters?
When it shows 'yes' for 'Distortion Corr Params Present' it means the camera had a correction profile for that lens available when the image was shot. It does not mean that the correction profile data is included in the image file created by the camera. It also does not mean the correction parameters were actually used to process the raw data from the sensor when producing the jpeg in -camera. 'Present' only means it was in the camera's data storage at the time and available for use at the time the photo was taken.
"Distortion Correction: None' means that even though there was an appropriate profile available at the time the image was captured, it was not applied to the raw data from the sensor when it was converted to a jpeg by the camera's internal processing.
Since the lens correction profile itself is not included in the image file, to apply correction after the fact using Lightroom or any other app, the application needs to have a correction profile for that camera/lens combination available within the application's data files. The correction profile used by the camera and the one used by the post processing application may or may not be the same or even similar. It all depends upon the source of each profile and whether the manufacturer of the camera and lens provide those profiles to the developers of third party products such as Lightroom.