Android reserves UID range 10000 to 19999 for apps - user, system or framework. u0_a12 doesn't indicate a user owned application, it simply means UID 10012 which can be assigned to any app. On Android every app is assigned a unique non-zero UID. No app can run with root privileges, including system apps.
UID 0 (root) is the privileged user in Discretionary Access Control (DAC) but be noted that even a process running with UID 0 can be non-privileged or one with non-zero UID can be privileged. Refer to Linux capabilities, particularly Ambient Capabilities.
However Android's Java framework doesn't rely directly on DAC very much, it has its own privilege control mechanism through permissions e.g. Storage, Camera, Internet etc. Manifest permissions have different Protection Levels. Some are granted without asking user, some others require user's approval to be granted or denied and some are reserved only for system use. For more details please see this answer.
Google Mobile Services (GMS) make use of both; application layer and some features only available to framework/system/privileged apps. For instance Play Services has android.permission.INTERNET which is granted to every app that requests for it. But it also has android.permission.READ_LOGS (1) which has protection level signature|privileged and can't be granted to user installed apps. Similarly GMS Core has unrestricted internet access even in Data Saver and Battery Saver modes (2) which is also possible only for framework apps.
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