How can I seamlessly make my phone a network drive? Back when I had an LG G2, it had this awesome feature called Wireless Storage. If you're not familiar with it, it essentially allowed you to tap a button to instantly turn your internal storage into a drive on your local network. You could then go into Windows Explorer, type in the local IP and password Wireless Storage provided, and be able to browse your phone exactly as if it was connected over MTP/USB or Bluetooth (but in my experience, I found it to be far faster and more reliable).

Now that I have a Galaxy Note 5, is there any way to recreate that same wireless storage feature, or at least come close to how seamlessly it worked?
There are several apps in the Play Store that can do this. One I've had some luck with is Samba Server.  To see other options, search the store with keywords like file server. Some functionality will require a rooted device, so YMMV.

Each of these have their pros and cons. I recommend trying a few to see which fit your specific situation best. Hopefully one of the free ones will work best for you!