How do I fix App Store asking for Gmail password and 'Security Restriction' after iOS update?

The last update has tied my device in knots. I'm ready to toss my entire cadre of Apple devices out the window - after the update I started to notice many problems. 1. The App Store asked for the Google Password and would not accept it. I was unable to download any new apps. 2. Media and Purchases had vanished from my settings so I could not alter it. 3. Two Factor Authentication stepped in and blocked any changes from my device until July 13 (!!!!) as a "security measure". 4. The "Reset Password" option for Apple would not complete - I would get to entering my phone number and it would reject it and say "Error has occurred password reset may not happen at this time." I was unable to reset my Apple Password from the phone - thanks to the "security restriction". This all happened immediately following the last update. I managed to figure out that when it asks for my Apple password it meant the password for the device, so I switched to the Mac and finally - with help from a real person at Apple - was able to reset the password. Without Apple's help I figured out how to make Media and Purchases reappear and reset that and my "Sign in and Security". Email was correct. Password was correct in all spots. I thought it was okay. Till last night - Tried to download an app and Voila, it asks for my Gmail password. I went to AppleCare and dealt with the completely useless AI and by accident got Eric, one of their "level 4 supervisors." He said the screen sharing was not working but had a hunch the problem was in the App Store settings. When he tried to set up screen share I waited 25 minutes and the phone went dead. Needless to say the AI "being" refused to reconnect me. She didn't know anything about what was wrong (despite 4 calls to AppleCare in the last 48 hours) and would not accept a case number. I gave up on her. I reset the App Store settings - again - checked the Media and Purchases and reset that and got the two devices logged on with the same passcode. I thought I was home free. This morning it started again with the App Store. I am going to change my gmail address to iCloud as primary and see if that shuts the thing up. It was so seamless before....it would see my face and I was good to go for a download. Even though Face ID is enabled it doesn't even try to use it. Because I could not get Apple to "verify" me - despite having all the right answers put in - I set up two physical security keys as backup for the Mac and phone, something I've tried to avoid. I'm ready to throw this thing off the deck - the sad part is it is only about a year old. The first engineer admitted there were "some problems with the update" but said "no one has had all this happen on one device..." she acknowledged the update was how it got started. Any ideas? I want to ditch the phone and am ready to start asking for one that is clean. Don't tell me to wipe it, I've already done that twice to no avail. My device is a 16 Pro, a Mac Air and (an iPad that I never use)

[Re-Titled by Moderator]

Original Title: Lasts update totals the ability of my phone to download apps from the App Store, phone is now restricted till July 13 "for security reasons."