I think you are searching for the One Shot focus mode. In that way it doesn't matter where you set your focus point (in this case the center) it should stay there and focus every time you press the shooter button.
Like other comment said it, there is more "advanced" ways to personalise the way autofocus works but this should solve your problem for the moment :)
This article explains the focus modes in a easy enough way:
I can’t/don’t know the technicalities but I know that a camera body you buy once and update it after 5 or more years so because of that I would go for the A7r III. I’d say youtube videos can help you to understand the differences between those models.
Very late answer but I hope is still helpful. I use capture one and Photoshop. On capture one I brought down the shadows quite a bit and controlled the white balanced then on Photoshop I did a levels correction (to adjust what’s the brightest area and what’s the darkest area) and the final touch was adding an overelayed black and white filter where I manually adjust reds, yellows and greens to add contrast to the picture.