For the highest chance of getting important data back in a situation like this, it would be best to find a reputable company that has experience fixing this for other people.
I would look for phone repair specialists first, to see if you can get the phone turning on again.
And if not, there are (pricey) businesses that can do data recovery on the storage chips themselves, but you may run into issues with encryption. From my quick research, it looks like the Note 4 was released with Android 4.4, which is after Google had implemented full-disk encryption. I'm not sure if it's enabled by default on your Note 4, and software updates over the years may have enabled it afterwards as well.
I wouldn't recommend attempting to swap the storage chips on 2 phones yourself, unless you have some equipment, and recovering your data isn't super critical. Here's an entertaining video on what the process of soldering these types of chips can sometimes look like: https://www.youtube.com/watch?v=Shn7LdIrViQ
My overall recommendation is call a few businesses, see what their professional opinions are, and decide if the price would be worth it to you. It would probably still be cheaper than buying a few spare practice-phones and trying repairs at home.