NeilC you don't airdrop the backup file as well as all the songs. You only need to airdrop the one backup file. That's the point of a (full) backup. If your backup file is in iCloud then you don't need to use airdrop at all. Inside ST3 on your iPhone, go to settings > restore backup. Now navigate through the file system from the file selector that pops up and find your backup file saved in iCloud. In theory this is all you need to do.
If you get problems using iCloud (because it's much slower sending data over the internet and could timeout, or for some other technical reason) then you could try the airdrop method. Airdrop will send a file directly from one Apple device to another Apple device over bluetooth and wifi. The trick is knowing what to do with the file once it arrives at its destination.
I feel that Apple is maintaining iTunes on PC for compatibility reasons and expect it will be discontinued at some point. Since they removed app-syncing, it's not all that useful anymore. What we really need is an iOS file manager, which unfortunately for PC users isn't officially available. Apple doesn't allow PC users to access app folders such as Stage Traxx's directly from Windows. That's why you're using iTunes File Sharing, which is Apple made and approved.
The process in ST3 is somewhat more complicated for the less tech-savvy users as @peter has designed ST3 to work hand-in-hand with iOS Files app. On the other hand, it isn't a bad thing to learn how the Files App works, as it will give you some superpowers on you iDevice as you're used to having as a PC user. 😄 I must say that Files is quite cumbersome and frustrating for an advanced user, but it is the only way you have to do certain things. In the old days of iOS devices there wasn't any Files App, but as it's becoming more capable as a computer replacement for some users it had to get this functionality eventually.