Maybe 'The Expanse'. It presents a highly advanced future where communication technologies like video chat are likely to be common. The show's detailed world-building might include such features.
One such series could be 'Star Trek'. In this franchise, characters often use advanced communication methods, including video chat-like technologies.
The 'Black Mirror' series sometimes incorporates elements of futuristic communication, including what could be considered as video chat. The show explores various dystopian and technological scenarios.