Can I use the same USB-C port for power delivery and video at the same time?

"Is this how USB-C works?" Short answer - Yes.

I am currently doing exactly that with a Lenovo USB-C dock and an HP laptop.

I get home and plug 1 USB-C cable into my laptop, and the mouse, keyboard, webcam and monitor all get connected at the same time, as well as charging the laptop. This has the added benefit of allowing me to use all those devices with any other laptop, and my Samsung phone to enable DeX.