Just trying to take it step by step.
Installing a catch can on that engine is pretty straight forward. If nothing else, get one of these:
https://www.amazon.com/gp/product/B086H9DGQQ
Though I'm pretty sure there are ready make kits from ADD W1 and other manufacturers for the Sonata 2.4L GDI.
Once you have a few miles with the catch can, you can look what accumulates in it, and how much blow by you have. It's far easier to do it this way than guessing. A catch can will also help clean your pistons and intake valves. Slowly all the gunk will burn off. Your oil will also stay cleaner for longer in the crankcase. I don't think Valvoline Restore & Protect will do anything for you.
I think that the oil control rings are gunked up. It's gonna take some work to clean them up. Installing a catch can is very important to keep those rings clean. Oil alone won't solve this problem.