I solved it for my issues, but solutions may not work for everybody. The sign-ins on 17.0.2 are getting stuck on an iCloud "Terms and Conditions" update that requests your agreement.
If you already have the accounts loaded, and they only need passwords, when you enter the password and the Terms & Conditions prompt shows up, say "Not Now". DON'T agree at this point as it's not registering your agreement in most of my attempts. Back out of the submenus to Settings. Near the top you will see you've got a new badge(s). Mine is gone now or I'd give a better description. Follow the badge and it's asking you to agree to those same Terms & Conditions again. If you agree here, it WILL register you agreed and now your accounts will magically load into mail! In one case I did have to restart the mail app and the whole phone, but then the account showed right up in mail. If you have multiple accounts that each need to agree, it may not look like your agreement is going through, but it is. It's just continuously loading the same request over and over until you have done it once per account that needed it.
If you are adding a new account from scratch, it's more messy. It's getting stuck on the same thing, but it's never prompting you for the agreement, so you don't know and there's no way to agree. I got lucky and hadn't erased my old device yet, and it still had the account active that I was trying to add to the new phone. So on the OLD device the Terms and Conditions agreement prompt popped right up and I could agree. It probably badged in the settings too, but I didn't think to look. I was able to agree on the OLD device, then went back to the NEW device, and it let me add the account in flawlessly and fast this time. No getting stuck. No prompt to agree or not. If you don't have a previous device with the account still on it, I would suggest adding it on an older device/ios just to see if you can get the T&C prompt. I'm not sure if the problem is from iOS 17, or from the hardware, or from some combination of those, etc., so try what you have access to, going backwards newest to oldest.