I'm used to shooting Nikon, where when you take a photo it shows a preview of the image on the main screen for a few seconds, or until you soft tap the shutter again. Is there a way to implement this in the Sony A7Riii? Right now it goes right back into live view immediately, without a preview of the image I just took.
The feature you are seeking is Auto Review. It is located in the menu under Display/Auto Review. From page 69 of the manual (pdf):
Auto Review: Sets auto review to display the captured image after shooting.