Hi,
Variables in TestComplete can reference any object or contain just a value. Thus it is not possible to predict what methods/properties can be used at the given line of code and thus Code Completion displays methods/properties for built-in objects only.
So, I would say that the observed behavior is correct and expected. (Yes, it is not completely convenient, but I have no idea of how it can be improved.)
P.S.
> I can manually enter Click() method, which I know for sure that works.
.Click() method will work only if the sought for button is found and continues to exist. Otherwise an empty stub object that does not contain .Click() method is returned and call to .Click() fails.
This is to illustrate how difficult it might be to implement Code Completion that will work as most of us expect.
