Record video to timeline during playback
DaVinci Resolve, Premiere, and FCPX all support direct video capture.  But depending on your hardware configuration, operating system, and camera, you will most likely need a video capture card or external capture device also.
Most computers don't come with a way to get video into them, they come with ways to get data into them.  HDMI ports are one-way, so you need an HDMI or SDI input, or a way to convert HDMI/SDI to data, and bring it in through USB, Thunderbolt, or PCIe, etc.  Webcams, whether internal or external will need a software driver to communicate to the NLE.  Generally, inbuilt webcams come with their own recording software, and computer manufacturers (hopefully) guard access to the camera. So for built-in webcams, you will need software which has access to your computer's hardware.  As Far as I know, FCPX can access FaceTime cameras, but Resolve and Premiere cannot.  For tethered ones, you'll need drivers supplied by the webcam manufacturer.