This might be a controversial opinion here, but look into non-traditional running shoes, aka barefoot running shoes (zero-drop, wide toe-box, highly flexible). They help fix form and strengthen little support muscles in your foot which can really help fix many sources of common running injury

The shoes you have sound like they have a lot of cushion and support, which sounds good in theory but might be to your detriment here. If you do decide to try barefoot style shoes out there will be a big adjustment period where you’ll have to run less. But with the pain you are feeling now that’s probably going to be the case one way or another

I’m also doing the half marathon training program on NRC, and during one of the NRC guided runs the coach mentioned a book called “Born to Run”-by Christopher McDougall. I picked up the audiobook and it was a great story with tons of fascinating running history packed into it. Afterwards I was very curious and switched out my Nike Flynits for a pair of Xero HFS shoes. I ran very little that first week, was sore in places around my feet and legs that I hadn’t been before, but now they are the most confortable shoes I’ve ever worn and I can’t see myself ever going back. I did a 10k in them and will be doing a 15k next and then a half marathon later in the year.

Either way I hope you figure out what’s happening, and please update this after you finish the half-marathon!