How can I find out a portable external hard disk's hardware details from within macOS?
There is the following command.

system_profiler SPStorageDataType


You will have to parse the output. For example, I have a external HDD with a single volume named RONSPASPORT. The output relevant to this drive is given below.

RON2PASPORT:

  Available: 29.27 GB (29,266,157,568 bytes)
  Capacity: 500.11 GB (500,105,216,000 bytes)
  Mount Point: /Volumes/RON2PASPORT
  File System: Journaled HFS+
  Writable: Yes
  Ignore Ownership: Yes
  BSD Name: disk2s1
  Volume UUID: BD65890D-BBAB-357A-B073-6B24625466F5
  Physical Drive:
      Device Name: 5000BEV External
      Media Name: WD 5000BEV External Media
      Protocol: USB
      Internal: No
      Partition Map Type: MBR (Master Boot Record)


From the output, one can see this is a WD 5000BEV.

Also there is the command below.

system_profiler SPUSBDataType


For the same external HDD, the following output is relevant.

        External HDD    :

          Product ID: 0x0705
          Vendor ID: 0x1058  (Western Digital Technologies, Inc.)
          Version: 1.75
          Serial Number: 57442D575836304139326384913837
          Speed: Up to 480 Mb/sec
          Manufacturer: Western Digital 
          Location ID: 0xfd130000 / 6
          Current Available (mA): 500
          Current Required (mA): 2
          Extra Operating Current (mA): 0
          Media:
            5000BEV External:
              Capacity: 500.11 GB (500,107,862,016 bytes)
              Removable Media: No
              BSD Name: disk2
              Logical Unit: 0
              Partition Map Type: MBR (Master Boot Record)
              USB Interface: 0
              Volumes:
                RON2PASPORT:
                  Capacity: 500.11 GB (500,105,217,024 bytes)
                  Available: 29.27 GB (29,266,153,472 bytes)
                  Writable: Yes
                  File System: Journaled HFS+
                  BSD Name: disk2s1
                  Mount Point: /Volumes/RON2PASPORT
                  Content: Apple_HFS
                  Volume UUID: BD65890D-BBAB-357A-B073-6B24625466F5


This provides more information, including the serial number.


  Note: The system_profiler command has the option -detailLevel level where the level can be mini, basic or full.