I'm not sure I see what you are talking about in the video, it seems to react instantly when you press the shutter then it displays the image briefly afterwards before going back to showing the view through the lens. But I am probably not seeing what you are trying to convey in the video. I tried my camera and I see no delay?
On a side issue I have had issues with the 60mm macro and getting it to focus on subjects that are further away after shooting close in. It will try to achieve focus and lock onto particles isntead of getting to the subject further out. - SO I tried S-AF + MF and purchased a focus gear for the lens. The problem is that takes a lot of turning of the focus ring to change any appreciable distance for example to move from focusing at 200mm to 600 mm takes one full turn - but if you place the camera in the housing the gearing on the focus knob is 5:1 reduction, so turning the focus ring on the lens one turn takes 5 turns of the knob on the housing. It is too slow to be useful you can't even tell whether the focus is getting better or worse at that gearing.
The only way "MF"is really practical is to AF to approximate focus and rock back and forward till it comes to focus. I almost universally rely on AF using small AF points and use C-AF+TR on back button focus and find that reasonably reliable.
I know it is hard to see, but if you hear carefully you'll see lag when I turn on the peaking. I tried even more, and it seems that it happens only in low light. If there is enough light, no lag occurs, but in low light with peaking on it always happens.
As a side note, you are brave to shoot with TR

It always focuses on the particles with me. May I ask which settings are you using for it?
Inviato dal mio ELE-L29 utilizzando Tapatalk