Hello @RequelP-2901 ,
This is actually due to security options on Microsoft Accounts. Even if we think everything is secure still there could be attacks going on in the background. I will give you example for my own Microsoft Account. It shows two attempts from some China location but I have never even logged on from any virtual server in China so there is no question of it being a valid logon . You can check this for your account on the Recent logon activity page.
It is probably some malicious attempt to brute force into my account. Thanks to the security on Microsoft Account , my account is safe. This happens a lot in general hence its important to be safe. However I can suggest you a few ways so that you do not see any prompt on your 2nd device.
If you have a surface device you can add the device directly using the portal using the devices page on your Microsoft Account portal . This page lists all your devices.
The easiest way is to logon to the computer using a browser session and if there are no cookies , it would give you something like following prompt which will be a MFA prompt as the system does not trust your device. You can select the option Dont ask me again on this device. And this would not prompt for MFA again as this device will be marked trusted.
Another way is to add an account using Windows Settings App . Click start > Settings > Accounts
You can even try to logon to the Mail application using your Microsoft Account credentials. I am assuming that you have windows 10 . however browser method must work on other older version of windows as well. this answer is based on that . You can check the article on how to add a trusted device to your Microsoft account as well. You should see the option I sign in frequently on this device . Dont ask me for a code.
This is similar to other options above but works most of the times. Sign in to any Microsoft Application like onedrive/onenote etc. using your Microsoft Account on your Iphone/Windows/Mac computers and once you have added them as trusted , you should not see this issue anymore. Check the Devices page on the Microsoft Account portal to confirm.
I hope one of the above methods should work for you and this should get resolved. In case the information provided is useful , please do accept it as answer so that it is helpful to other members of the community. In case you still have any query , please let us know and we will be happy to help .