We are trying to assess how many images are stored locally on Wikimedia sites, rather than hosted on Commons. We also want to better understand what templates they are using for their metadata.

Does anyone know where we could find reliable statistics and links for these non-Commons files?

Does not ring a bell to me. :-(

Closer I recall  is the opposite  − projects that do not need to be checked for non-CommonsFiles
<https://commons.wikimedia.org/wiki/Commons:Turning_off_local_uploads>
 
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Jean-Fred