The level of inaccuracy in a regular clock resulting in drift is orders of magnitude greater than any amount of time dilation you would experience.

This is the reason we use extremely high precision clocks (like atomic clocks) and then synchronize everything else with them. Even your phone's clock would drift noticeably over a period of a few months if it never synced with some network server.

The NTP protocol exists precisely for this. There are entire companies that specialize in providing and maintaining synchronized wall clocks for facilities like hospitals, schools, and other organizations.