Hello Ageless5,
Thanks for posting in the Apple Support Communities.
It sounds like you're being prompted to sign in with your Apple ID when you pair an AirTag, although you're already signed in. Is that correct?
If we have that correct, let's confirm you have the latest iOS version installed to see if that may be related to what's occurring. If an update is available, be sure to back up your information before installing this. You can locate steps to help with backing up, and updating, here: Update your iPhone or iPad - Apple Support
If you have the latest iOS version installed, give the steps below a try to see if the results change. In addition, check if you're using a managed Apple ID as that would prevent the AirTag from being set up. You can locate additional details to review here: Set up your AirTag using your iPhone, iPad, or iPod touch - Apple Support
If you can't set up your AirTag
1. Make sure that your device is ready for setup.
2. If the setup animation disappeared, press the side button or Sleep/Wake button on your iPhone to put your device to sleep. Then wake and unlock your iPhone. Wait up to 15 seconds, and the animation should reappear.
3. If you have multiple AirTags to set up, make sure that only one is near your device at one time.
4. Remove and then replace the battery in your AirTag.
5. If your AirTag still won't connect to your device, reset your AirTag.
Learn what to do if you see a message that says the AirTag is connected to another Apple ID.
If you continue to experience this message with everything appearing to be set up correctly, contact Apple Support directly to check into this with you.
Take care!