I think focus peaking has become common now throughout the photography industry in all the major brands, both in their DSLRs and their mirrorless cameras. Isn't it great? Whoever first developed it is someone to whom I am very thankful! LOL!
On my new camera, when I got to the menu setting which offered Manual Focus Assist I clicked the button to activate it, but after using it a couple of times while shooting with manual focus quickly disabled it; this is one of those features which I need to go back to after I've become more comfortable with all of the camera's functionality and features and with my new lenses, rather than trying to deal with a bunch of new things all at once. I know it can be a very useful tool but I'm just not ready to utilize it yet.
As for fine-tuning in manual focus after using autofocus, that in the Sony system is called DMF (Direct Manual Focus), where one can first focus using autofocus to get into the right ballpark and then more precisely adjust using manual focus -- this, along with Focus Peaking, is extremely useful when shooting in macro!