Sony is preparing a new update for the PS4 Pro that will allow the Media Player to playback 4K content, with some other tweaks being thrown into the update for the PS4 Pro.
You can playback content from a USB stick or home server, like a PC or NAS, but 4K content will be allowed through PSVR as well. USB storage will need to be formatted, as the extended PS4 storage can only be used for saved games/apps - and can't be used to store or save videos. Sony adds: "For those of you that own a PlayStation VR system in addition to PS4 Pro, Media Player will also update to support playback of 4K VR video content".
Sony continues: "PS VR's display resolution is 1920 x RGB x 1080, therefore 4K VR videos will be displayed in a higher image quality compared to HD VR videos. Capture stunning 360 degree 4K footage, and then immerse yourself in that footage in VR at home - just as if you're right back in the scene you shot".