I would like to say thank you to @Mr.Mochocho. We spent several hours on the online chat to find out what was happening on his computer. And we found that. Without @Mr.Mochocho’s help and patience it would be very hard to identify and resolve the issue.
For those encountering difficulties with the detection of the Electra One controller in the app.electra.one web editor, it is highly recommended to update the controller to version v3.2.7 or a later release. Detailed instructions on how to update can be found at Updating Electra One mkII.
Some E1 serial numbers (which are based on serial numbers of the CPU inside the unit) invalidated the SysEx JSON message that E1 uses when it initiates the connection with the web editor. As result, these units seemed to work just fine but could not connect the editor application.