I don't know of any work done as you've asked: CGMs seem to have only just registered as far as research goes, but you'll find a lot on keto/low carb with BGs tested by HbA1c. You might speculate about why this is - CGM inaccuaracy, cost, HbA1c being the "standard" test, and so on.
Plenty of stuff arpound on low carb/keto eg
This has a good number of references itself.
Everything else I know is anecdotal - my own CGM use was informative in giving me an idea about what happened while I wasn't testing, or couldn't test - sleeping/exercising, that sort of thing, but was less good (in my opinion) in tracking actual BG values when compared with fingerprick tests.