Hey there! Congratulations on your new Mac!
I am assuming these are the Apple apps that are giving that error (Pages, Numbers, iMovie, etc).
First try going to App Store, clicking on the circle with your Apple ID at the bottom-left of the page > purchased > and see if it allows you to click on accept apps under the Apple applications.
If it does not, no worries! You will want to delete the applications and then reinstall. This will place the latest version on them as well as be under the Apple ID you signed into the App Store with.
To delete, you can go to Finder > Applications and drag to the Trash bin > Empty or go to Launch Pad (rocket ship icon) > hold down on the app until they all shake and the delete. https://support.apple.com/en-us/HT202235
To reinstall, you can go back to under your purchased items or look up and there will be a cloud with a down arrow. You can click all and do not have to install one by one. HT201272
Hope this helps!