Do give us a Web link for where this kit is available! Edit: OK, found it, but can't find a sensible description of pricing. Seems to be a "work in progress" but you clearly have one!
No, you need the connector leads as you show for the display and the other "sensor" modules, even if you so not separate the parts. It appears, looking at a higher resolution photo on the Amazon page, that the display is pre-connected. :sunglasses: So remove your connector cable.
The Expansion Shield is pre-wired to the "UNO" because there is only one way for it to be connected, but how you connect some of the other parts is optional.
Suggest you install the more-up-to-date HD44780 library using the Library Manager in the IDE and use the examples provided with it to access the LCD display rather than whatever else may have been provided with the kit. :grinning:
Make sure all the DIP switches are off!
You will likely need a proper 5 V regulated power supply to operate the servo - or any similar thing connected to this system - feeding to the "5V" pin rather than the USB jack. Do not attempt to power it via the "barrel jack".