Cannot sync new Apple Watch with iPhone due to 'spinning wheel of death' when updating Apple Account settings for end-to-end encryption

I bought a new Apple watch 10. I am trying to sync my iPhone 14 to it.

It says I need to update my Apple account settings so that my iPhone can use into end encryption. When I select continue, I just get the perpetual spinning wheel symbol on the screen with no resolution. I checked, and I am using the most updated version of iOS. How do I fix this?

[Re-Titled by Moderator]

Original Title: I cannot sync a brand new Apple Watch with my phone because it says that my Apple account settings need to be updated so this iPhone can use into end encryption. When I try to do this on my phone, I only get the spinning wheel of death.