DWG file format is the same on PC and on Mac - that is true. But File Systems are different and it is also - true. This is OS specific incompatibility.
Mac OS uses HFS+ file system and Windows uses NTFS file system. Both OSes can read different file system, but cannot write to it without special (additional) software drivers.
In order to be able to use external hard drive on Mac and on PC (Windows) you need to Format it with FAT32 file system, because both macOS and Windows can read and write files, including DWG files, to the disk formatted with this file system.

Maxim