The enclosure exposes the drive to the computer as an Advanced Format 4Kn device, allowing the use of MBR for compatibility with Windows XP systems. When the drive is removed from the enclosure, the change in logical sector format results in an invalid partition table.
External hard drives larger than 2 TiB in capacity often expose 4K sectors directly to the operating system. The 2 TiB limit commonly associated with MBR is tied to the traditional 512-byte sector size; 4K sectors are eight times as large and therefore extend the MBR limit to 16 TiB. This allows the use of MBR on disks larger than 2 TiB in capacity, enabling use on Windows XP and other systems which do not support GPT.
The underlying hard drive uses 512-byte sector emulation for compatibility with legacy systems. This means that while the disk physically has 4K sectors, the immediate host device (in this case, the enclosure) sees 512-byte sectors. However, to perform the aforementioned MBR expansion and enable Windows XP compatibility, the enclosure makes the drive appear to the computer as having 4K native sectors.
When the drive is removed from the enclosure, the 512-byte logical sectors of the underlying 512e disk are exposed. This results in an invalid partition table that cannot be correctly interpreted. The 746.52 GiB value you gave for the last "partition" when the drive is connected directly is precisely the amount of space that lies beyond the 2 TiB limit for MBR drives with 512-byte sectors.
More details about the implications of this conversion are available in this blog post.