Hello Paul, 
thanks a lot for providing your thoughts on the matter.
That was my thinking as well. So glad about your confirmation. 
Today for example I couldn´t hear the sound at all - just due to the fact that I was taking a few steps back from the switch of the power-supply. A loud enough sound made by my shoes to drown out the (already barely perceivable) sound. 
Thanks for the link, Paul.
In Lubunutu 20.04 the respective command is  gnome-disks .
I tried what is suggested on the page you referred to. Yet the button SMART Data & Self-Tests…  is greyed out for the external disk and thus not available.
It would work with the internal disk though.
I think this is because of what ubuntuusers.de are talking about on Festplattenstatus › Wiki › ubuntuusers.de  when referring to external USB housing:
External USB enclosures usually have a converter chip (e.g. a USB-SATA bridge) that functions as a converter between the various interfaces / protocols.
It can happen that an S.M.A.R.T. query is not correctly implemented:
sudo smartctl -A /dev/sdX
/dev/sdX: Unknown USB bridge [0x1e68:0x001b (0x000)]
Hard drives in external enclosures appear to be unsupported, although they are definitely S.M.A.R.T.
This can be remedied by using a special option:
sudo smartctl -A -d sat /dev/sdX
(translated from German)
As I have smartmontools installed on my system I made use of the command
sudo smartctl -H -d sat /dev/sdb
for  a quick test:
smartctl 7.1 2019-12-30 r5022 [x86_64-linux-5.4.0-91-generic] (local build)
Copyright (C) 2002-19, Bruce Allen, Christian Franke, www.smartmontools.org
=== START OF READ SMART DATA SECTION ===
SMART overall-health self-assessment test result: PASSED
Looks good, I think. 
Plus: I regularly (every day, at the start of each session) run the command
sudo smartctl -A -d sat /dev/sdb
in order to check the attributes of the HDD (see: Festplattenstatus › Wiki › ubuntuusers.de ):
smartctl 7.1 2019-12-30 r5022 [x86_64-linux-5.4.0-91-generic] (local build)
Copyright (C) 2002-19, Bruce Allen, Christian Franke, www.smartmontools.org
=== START OF READ SMART DATA SECTION ===
SMART Attributes Data Structure revision number: 16
Vendor Specific SMART Attributes with Thresholds:
ID# ATTRIBUTE_NAME          FLAG     VALUE WORST THRESH TYPE      UPDATED  WHEN_FAILED RAW_VALUE
  1 Raw_Read_Error_Rate     0x002f   200   200   051    Pre-fail  Always       -       0
  3 Spin_Up_Time            0x0027   113   108   021    Pre-fail  Always       -       5316
  4 Start_Stop_Count        0x0032   098   098   000    Old_age   Always       -       2684
  5 Reallocated_Sector_Ct   0x0033   200   200   140    Pre-fail  Always       -       0
  7 Seek_Error_Rate         0x002e   200   200   000    Old_age   Always       -       0
  9 Power_On_Hours          0x0032   088   088   000    Old_age   Always       -       8857
 10 Spin_Retry_Count        0x0032   100   100   000    Old_age   Always       -       0
 11 Calibration_Retry_Count 0x0032   100   100   000    Old_age   Always       -       0
 12 Power_Cycle_Count       0x0032   099   099   000    Old_age   Always       -       1781
192 Power-Off_Retract_Count 0x0032   200   200   000    Old_age   Always       -       159
193 Load_Cycle_Count        0x0032   179   179   000    Old_age   Always       -       63576
194 Temperature_Celsius     0x0022   131   105   000    Old_age   Always       -       16
196 Reallocated_Event_Count 0x0032   200   200   000    Old_age   Always       -       0
197 Current_Pending_Sector  0x0032   200   200   000    Old_age   Always       -       0
198 Offline_Uncorrectable   0x0030   100   253   000    Old_age   Offline      -       0
199 UDMA_CRC_Error_Count    0x0032   200   200   000    Old_age   Always       -       0
200 Multi_Zone_Error_Rate   0x0008   100   253   000    Old_age   Offline      -       0
So I think (and hope) everything´s fine… 
Many thanks again for your help, Paul.
… and many greetings from Rosika 