In die 80ies/90ies with analog film, I found lenses from Zeiss (Contax cameras) and Leica (M&R) to have very often this 3D effect. Especially in combination with the slide films Fuji Velvia and Provia 100F.
At that time there was a significant image quality difference between the excellent Zeiss/Leica lenses and the crowd of Canon/Nikon/Minolta/Pentax/Sigma etc . Sony did not exist in photography in these decades.
Then Sigma decided to offer DSLRs. This alone was already a sensation. But on top of that, they offered these cameras not with a traditional Bayer sensor like the rest of the world, but with a Foveon sensor. Foveon was still an independent company back then (did you know that a Kodak camera existed with a Foveon sensor?).
The first Sigma DSLR camera was the Sigma SD9 with a Foveon sensor.
This was for me the first time when I saw this 3D pop effect also on images not shot with Zeiss or Leica lenses. On almost every image shot with the Foveon sensor. For me this was crazy, because the Sigma lenses were not different. If I used the same lens on a Nikon body, there was no 3D effect at all. So only the sensor was the reason.
From that moment on I was a die-hard fan of the Foveon sensor.
I founded the first and only Sigma only user community in German and English to show others that you can have Leica like (and often even better) image quality for a very low price (with some disadvantages in postprocessing).
This 3D experience continued from the Sigma SD9 to SD10, SD14, SD15 and SD1. The Sigma compact cameras (DP) had this too, especially the Sigma DP Merril 1, 2 and 3. BUT the DP cameras after the DP3M had a different designed Foveon sensor and due to this, this 3D pop effect almost disappeared (in my view) in all successors of the DP Merrill compact cameras.
Having had this experience with the very different setups I concluded for me, that there is more than one factor which leads to this 3D pop effect and it has nothing to do with DOF or background seperation.
In my view, if it comes from the lens, it has something to do with microcontrast. It is a certain rendering. Even if you shoot at F11, you get this 3D effect.
But for me most important is the sensor. That most cameras have nowadays no AA filter anymore helps. But this 3D transparancy reality of a Foveon sensor is still unmatched.
The Foveon sensor not only gives a Pop effect, it shows a clarity, a realism in the image that gives you the impression that you look through an open window instead of looking through the closed window.
You have the impression to touch the subject you are shooting with your hands. It is not an image anymore. It is real like it would be in front of you.
The downside of the Foveon sensor is high ISO noise, colour shift and it is difficult to correct it in the Sigma software SPP. Lightroom supported only the first version of the Sigma DSLRs, later model not anymore.
I have to see whether I can dig an old Sigma photo out of my backups to show you what I mean.
This is the reason why I was so excited when I heard on the press conference at Photokina 2018 about the L-Mount alliance. Because with Sigma the Foveon idea could continue. I created this L-Mount forum in the first night after this press conference while I was still there in my hotel room in Cologne/Köln. That was a lot of adrenalin at that time.