Additional verification required but no field to type in password and code

I have an iPhone 4 and I’m trying to get info from it before I use it for other things. I’m trying to get it connected to my Apple ID with my iPhone 7. I was just using an app on the iPhone 4 that had nothing to do with the account ID, when suddenly a box asking for my Apple ID appears. Almost at the same time my iPhone 7 had a box with a little map and a message that says something is accessing my Apple ID at such and such location, or something like that, appears. It has the options “Don’t allow” or “Allow”. I tap allow. That box disappears and is replaced with a box that has a 6 digit verification code in it. A box opens up on my iPhone 4 saying there’s “Additional verification required” to authenticate my account. The options are, “Cancel” or “Settings. I go to settings and a “Terms and Conditions” for iOS and iCloud form appears with the options “Disagree” and “Agree”. I tap agree. Then agree again in another little box that appeared. Meanwhile on my iPhone 7 the box with the number for authentication is still there. On the iPhone 4, while it starts to verify, a box appears that says “Additional Verification Required” with the options “Cancel” and “Settings”. I tap settings, and a box appears, “Apple verification code required” with the word “Ok” under it. When I tap ok it crashes and the home screen appears. While the home screen is there, my iPhone 7 keeps sending verification numbers one after the other for about 3-5 times at a time. Then on my iPhone 4 the “Additional Verification Required” box appears with the options “Cancel” and “Settings”. I tap settings. It goes to settings and a “Terms and Conditions” for iOS and iCloud appears. There are options at the bottom, “Disagree” and “Agree”. I tap agree and the loop starts again. The box that comes up “Apple Verification Required” usually very quickly gets replaced with the “Additional Verification Required” box. It usually happens so fast I can’t tap “Ok” on the “Apple Verification Required” box. On the “Additional Verification Required” box, if I don’t tap anything it will be about 5 min before another authentication number comes up on my iPhone 7. Then it starts all over again in a wonderful fun filled loop. Yay! I’ve tried rebooting both phones. I got out of settings and came back in. I don’t want to do a hard reset unless it’s the only option because there’s info and pics I want to get off it. I was able to connect another iPhone 4 I have without any problems. If someone has some ideas I’d love to hear them. There are a couple of questions here that are similar but the answers go off in other tangents so while helpful in a lot of ways the info didn’t apply. Thanks