How can I move music from my iPhone to my laptop?

Earlier today, I had to do a surprise factory reset on my computer, and before doing so, I didn't have the chance to back up a lot of my data. So, any of the music that I had on my computer that wasn't from Itunes (transferred from CDs, purchased from online shops, etc) can only be accessed from my phone. In syncing with Itunes, all of the extra music on my phone will be deleted. This is okay for now, since I don't need to sync, but I know that eventually I will need to and I don't want to lose all of my music.
All that I can find online is information on how to move music from my computer to my Iphone. How can I do it the other way around?

As you have found out only music bought through iTunes will be restored when you log into your iTunes account. All other music is lost from the PC. Itunes only syncs to not from an iPhone

You can however transfer music from your iPhone to a PC with third party paid software.
just google iphone to PC transfer for some hits

Apple products don't let you do that.
however, there are paid (not free) software that can do it.
iTransfer and AnyTrans are 2.

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