Hello, Aristotle247. Thank you for posting your question to the Apple Support Communities. We understand that you are noticing this Apple ID message on several of your devices. We’re happy to help you find out what may be causing this and what you can do to remove the message.
Since you have already entered your password several times, we would next suggest restarting each device before trying again.
If needed, please also install any available software updates. We suggest creating a device backup before updating like this:
Update your iPhone, iPad, or iPod touch - Apple Support
If you continue to notice the same issue, please try to connect your devices to a different network before entering your Apple ID information again.
We hope that these suggestions help you. Please let us know if you have any other questions.
Cheers!