EFCS should mostly solve any vibration issues arising from the mechanical shutter, but it can result in asymmetric rendering of out-of-focus areas at fast shutter speeds and also lead to uneven exposure with tilt/shift lenses (with movements applied) again at fast shutter speeds. Flash can be used. Nikon limits EFCS to 1/2000s at least in my cameras. Fully electronic shutter avoids vibration issues as well as the bokeh issues of EFCS but it cannot be used with flash and it can result in rolling shutter if you have moving subjects, and banding in flickering artificial lighting. Mechanical shutter has less rolling shutter than fully electronic shutter, and no asymmetric bokeh issues, and flash can be used, but it can cause vibration.
Pick your poison!
I don't yet have any Z camera but use the D850 which allows EFCS use in Qc mode, and I find its use often leads to superior sharpness. I have not noticed significant anomalies in bokeh or evenness of exposure though I often use tilt-shift lenses (but usually in circumstances where the lighting is dim, the camera is on tripod and so the shutter speed is quite low, it might be e.g. 1/25s or thereabouts). I go to regular mechanical shutter mode when I need fast shutter speeds or faster response time (in mirrorless, EFCS should result in shorter shutter lag) or high fps, as those are limited in the D850 when using EFCS.
I guess there are no hard rules about the use of these different shutter modes. I would go about it like this: shoot auto EFCS until you run into a problem. A problem might be that there is vibration from the mechnical shutter and then select either full-time EFCS or silent, fully electronic shutter, depending on whether you have movement or artificial light, or change the shutter speed to where EFCS kicks in (slower speeds) or faster shutter speed so as to minimize the blur due to the shutter vibration. If you are going with a fast shutter speed, you may get some slight issue with bokeh or tilt-shift lens, and in that case, you can either choose a slower shutter speed or switch to mechanical shutter.
I guess what people would like is certainty that there is a mode which always gives the best results, but this is complicated. I am glad that Nikon offers an auto EFCS mode even if it doesn't always produce perfect results, so that at least shooting is easier and making choices and frequently changing settings is not required.