I don't have a case study, but a site I am working on pulled their contact pop-up widget that I put on because I couldn't make changes to the full size banner to overlay CTA. Leads went down by like 95%.
Look through Baymard’s articles though it’s usually focused on carousels and ad type banners, not banners as a whole. A few that come to mind (not sure if your ecomm or not)
IIRC, @Ross Hudgens posted a few months back about some research on how smaller hero images are better than the common/giant hero images most sites use. Maybe a little different than large banners, but directionally similar?
Haven't seen any but then again imho it als needs to fit the brand. Sometimes it might be good to be very visual, in others there's a better use of that space. Could you test?