0x87DD0006 appears when the console cannot sign you in to the Xbox network. Microsoft's own explanation is that there may have been a service outage just before you tried to sign in, and that is the most common cause. It is a sign-in and service problem, not a sign that the console hardware has failed.
If the status page is green, the network test passes, and no profile signs in, try signing in to the account in a browser to confirm the account itself works. If the browser sign-in works and the console still refuses, the console's stored sign-in data is the likely fault, so a factory reset keeping games and apps is the last local step before contacting Xbox Support.
Is 0x87DD0006 a hardware error? No. It is a sign-in failure, and Microsoft's first explanation is a service outage around the time of sign-in. Hardware is not part of Microsoft's published steps for this code.
Will removing my profile delete my games? No. Removing a profile removes the local sign-in record. Games, saves, and licences stay on the console, and signing back in restores access to them.
Why does it happen during a system update? Sign-in can fail while update services are busy or interrupted. If the code appeared during an update or first-time setup, follow Microsoft's system update troubleshooting instead of the sign-in steps.