To my best knowledge, no. A streamer called Destiny successfully uses a capture card from a company called Magewell with OBS and while he uses 1440p they do have cards supporting up to 4k resolutions. Another option which I don't know users of but exists is the Blackmagic DeckLink line.
However, neither seems to have Displayport inputs, only HDMI, (Dual-link) DVI and SDI ones.