How to correctly write Try..Finally..Except statements?

You just need two try/finally blocks:

Screen.Cursor:= crHourGlass;
try
  Obj:= TSomeObject.Create;
  try
    // do something
  finally
    Obj.Free;
  end;
finally
  Screen.Cursor:= crDefault;
end;

The guideline to follow is that you should use finally rather than except for protecting resources. As you have observed, if you attempt to do it with except then you are forced to write the finalising code twice.

Once you enter the try/finally block, the code in the finally section is guaranteed to run, no matter what happens between try and finally.

So, in the code above, the outer try/finally ensures that Screen.Cursor is restored in the face of any exceptions. Likewise the inner try/finally ensures that Obj is destroyed in case of any exceptions being raised during its lifetime.

If you want to handle an exception then you need a distinct try/except block. However, in most cases you should not attempt to handle exceptions. Just let it propagate up to the main application exception handler which will show a message to the user.

If you handle the exception to low down the call chain then the calling code will not know that the code it called has failed.