I found the answer myself. It appears that there is additional component which works just for this particular purpose called TEditDesigner
which makes all things related to editing trivial. Found the solution by looking into Demos folder (there are a lot of examples there for various things).
The solution:
Drop TEditDesigner
on the form and connect it to the TEmbeddedWB
using property EmbeddedWB
or use EditDesigner1->EmbeddedWB = EmbeddedWB1;
in code
Code that loads HTML and makes it editable then is the following:
EditDesigner1->ConnectDesigner();
UnicodeString html("<body><p>Hello world</p></body>");
EmbeddedWB1->LoadFromString(html);
// Optionally focus to it
EmbeddedWB1->SetFocus();
01 - EditDesigner_Demo (folder) shows a lot more things you can do with TEditDesigner
.