I would log into the yahoo website (yahoo.com and click mail button in upper right). To get as far as you did, I assume you did the initial login with <you>@cox.net username and old password, the set a new yahoo password. Make sure you can receive and send email in the yahoo mail website. Maybe leave this up while going to next steps...
Then, on your iPhone, you need to go to mail in settings and add a new account, selecting yahoo, and entering your <you>@cox.net as the user name. Somewhere (I forget just where) yahoo should ask for authentication and permission for your iPhone access. I don't think you can update your old iPhone mail for cox to yahoo; I think you have to create a new mail account on the iPhone. Don't delete your cox email from your iPhone until you have everything (like Notes which would be deleted, like I did😁 on my wife's phone). It should work.
You can also download the yahoo app to your phone. I did this, which might help with authentication sometimes. But I might delete it when the dust settles.
From this thread, just be aware that it seems that yahoo might be "protecting" us from .gov sites, even if you use them for 2-factor authentication (like social security).