A new device added to my messages

Hello nicolle149,

Welcome to Apple Support Communities. 

We understand that you’re concerned about the security of your device. We are happy to help.

While we understand that you have spoken to Apple Support, we just want to reiterate that you should enabled Lockdown Mode. You can find out more about Lockdown Mode here: About Lockdown Mode - Apple Support

"How Lockdown Mode protects your device

When Lockdown Mode is enabled, some apps and features will function differently, including:

• Messages - Most message attachment types are blocked, other than certain images, video, and audio. Some features, such as links and link previews, are unavailable. 
• Web browsing - Certain complex web technologies are blocked, which might cause some websites to load more slowly or not operate correctly. In addition, web fonts might not be displayed, and images might be replaced with a missing image icon.
• FaceTime - Incoming FaceTime calls are blocked unless you have previously called that person or contact.
• Apple services - Incoming invitations for Apple services, such as invitations to manage a home in the Home app, are blocked unless you have previously invited that person.
• Shared Albums - Shared albums are removed from the Photos app, and new Shared Album invitations are blocked. You can still view these shared albums on other devices that don’t have Lockdown Mode enabled. When you turn off Lockdown Mode, you need to turn Shared Albums on again in your device settings.
• Device connections - To connect your iPhone or iPad to an accessory or another computer, the device needs to be unlocked. To connect your Mac laptop with Apple silicon to an accessory, your Mac needs to be unlocked and explicit approval provided.
• Configuration profiles - Configuration profiles can’t be installed, and the device can’t be enrolled in Mobile Device Management or device supervision while in Lockdown Mode.

Phone calls and plain text messages continue to work while Lockdown Mode is enabled. Emergency features, such as SOS emergency calls, are not affected. 

How to enable Lockdown Mode on iPhone or iPad

1. Open the Settings app.
2. Tap Privacy & Security.
3. Under Security, tap Lockdown Mode and tap Turn On Lockdown Mode.
4. Tap Turn On Lockdown Mode.
5. Tap Turn On & Restart, then enter your device passcode.

When Lockdown Mode is enabled, you might receive notifications when an app or feature is limited, and a banner in Safari indicates that Lockdown Mode is on.

Lockdown Mode needs to be enabled separately on each device."

We also recommend these steps if you believe your Apple Id has been compromised: If you think your Apple ID has been compromised - Apple Support

"Gain control of your Apple ID

1. Change your Apple ID password
2. If your Apple ID password has been changed by someone else, reset your password.
3. Go to appleid.apple.com to update any of personal or security information that isn't correct or that you don't recognize.
4. Check with your email address* provider to make sure that you control every email address associated with your Apple ID. If you don't control an email address, work with your email provider to regain control or use a different email address."

Let us know if you have further questions.

Take care.

Same here in 2 Intel MBPs (2020 and 2012). The Apple ID account does have the same very old iPad Air (ME993LL/B; A1475; 1st gen. model; iOS v12.5.7, 16 GB, & VZW cellular (4G LTE) from 1/27/2015. Is this why? If so, then that message is confusing and scary. :/