Cannot sign in to iTunes Account on Mac with two-factor authentication

Well, I think that's it. I brought up iTunes on my laptop, which has Sierra on it, and, even though it wasn't the latest iTunes, iTunes did bring up the verification box after the password box on the laptop.

So... I basically need to update my iMac to Sierra, though I had been holding off..

Okay, several questions about this.

1. The link about "How do I sign in to my account using an app that doesn't support entering two-step verification codes?" refers specifically to third party apps in the example. This is iTunes we're talking about.
2. I tried the app-specific password generated at my AppleID account page. I clicked on Account in iTunes, then pasted in that password, and pressed OK. It did not take me to my Account page.
3. I tried putting in the verification code after my password with a space. In that case, I had to click Account, enter my Apple ID password, then hit OK, then wait for the code to show up on my iPhone, then hit Account again, enter my Apple ID password, press space, type in the 6-digit verification code, then hit OK. No error message, it just won't get me to my account page. At all.

It is absurd to me that iTunes is working this way. There is no update available. It isn't "older software" in that it has a 2017 copyright date. Is this because I'm on Yosemite?