It looks like Sony might have put some extra effort into making AF work with adapted lenses on the Sony a7RIII from the various Metabones Mark IV/Sigma MC-11 videos on the web. My Techart adapter still works great, but when using eye AF with it I get a lot of out of focus photos, yet the feature appears to work. Metabones Mark/Sigma adapters appear to be working well though.
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Sony a7RIII: B&H Photo / Amazon / Adorama
Sigma MC-11: B&H Photo / Amazon / Adorama
Metabones Smart Adapter: B&H Photo / Amazon / Adorama