I did nothing more than what I had specified above. I made AmiUpdate work. I specified the connection parameters, and I was able to retrieve the two files date_cmd-53.11.lha and Prefs_Time-53.11.lha.
All this is described in RAM:au.log
AmiUpdate 2.48 (17.1.2021) Part of the AmiUpdate suite
Log opened on 22-6-2021 at 17:02:49
17:02:49 Performing online version check...
17:02:50 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:02:50 Connected
17:02:50 Online version check completed.
17:02:50 Program started
17:02:50 Started system scan
17:02:50 Found host machine as: X5020
17:02:50 Synchronising with server: 'update.amigaos.net'...
17:02:50 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:02:50 Connected
17:02:50 Prompting user for login details...
17:03:04 Login cancelled
17:03:04 No logon details supplied, updating aborted
17:03:04 HTTPFetch error: No login details were found or supplied
17:03:04 Scan completed
17:03:04 Waiting for user input...
17:03:09 Starting uniconify...
17:03:10 Opening window...
17:03:13 Started system scan
17:03:13 Found host machine as: X5020
17:03:13 Synchronising with server: 'update.amigaos.net'...
17:03:13 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:03:13 Connected
17:03:13 Prompting user for login details...
17:03:24 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:03:24 Connected
17:03:24 Failed to get filesize from header, Content-Length: tag missing
17:03:24 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:03:24 Connected
17:03:25 Synchronisation successful
17:03:25 Scan completed
17:04:08 Creating working directory...
17:04:08 Created
17:04:08 Starting update of 'date_cmd-53.11.lha'
17:04:08 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:04:08 Connected
17:04:08 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:04:08 Connected
17:04:08 Preparing to unarchive: date_cmd-53.11.lha
17:04:08 Archive unpacked successfully
17:04:08 Trying to locate AutoInstall script..
17:04:08 'AutoInstall' script detected, preparing RollBack...
17:04:08 Executing AutoInstall script...
17:04:09 Script completed without errors
17:04:09 Cleaning up working directory...
17:04:09 Cleaned up without errors
17:04:09 Update finished
17:04:09 Checking for other entries in the same archive...
17:04:09 None found
17:04:09 Starting update of 'Prefs_Time-53.11.lha'
17:04:09 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:04:09 Connected
17:04:09 Trying to connect to: www2.hyperion-entertainment.com on port: 80
17:04:09 Connected
17:04:09 Preparing to unarchive: Prefs_Time-53.11.lha
17:04:09 Archive unpacked successfully
17:04:09 Trying to locate AutoInstall script..
17:04:09 'AutoInstall' script detected, preparing RollBack...
17:04:09 Executing AutoInstall script...
17:04:09 Script completed without errors
17:04:09 Cleaning up working directory...
17:04:09 Cleaned up without errors
17:04:09 Update finished
17:04:09 Checking for other entries in the same archive...
17:04:09 None found
17:04:09 Deleting working directory...
17:04:21 Closing program
Thank you guys and especially thank you... to the one who intervened on the server