What does an external hard drive do after it's been ejected?

FYI, I never unplug any external drive right away. I always wait at least 30 seconds or until the drive's LED stops blinking to ensure that the drive is no longer being accessed. I've found sometimes that macOS may still be attempting to flush the buffer and unmount the drive (even for an SSD). I really wish macOS still kept the "It is Ok to disconnect the drive" notification message since an external drive (even an SSD) is not always ready to be immediately disconnected. I've had a number of times where even waiting 30 seconds was not enough and I have received the notice "Drive was not properly ejected". Even when macOS is finished transferring data to a drive, the drive may still be handling the data internally....transferring data from the internal drive cache to its permanent storage location on the magnetic media (hard drive) or to the NAND memory chip (SSD, or even hybrid drives).

From my experience, once a drive is ejected (after macOS is finished with the drive which can take a bit of time sometimes), the drive is then no longer physically seen by macOS. At that point the drive is only receiving power. A hard drive will continue spinning, I've never left an ejected drive connected long enough to notice if there is any other activity...I would not really expect it, but like @muguy says, the drive's controller may be doing some internal housekeeping. I know SSDs will perform some internal maintenance and garbage collection when just sitting idle without any data connection.

The device remains powered, possibly spinning, and running fans, etc to regulate temperature. The onboard firmware may also run tasks on the drive to verify that it is working, checking for errors, moving cached data, etc.