If you can get to HDMI somehow (might be tricky with a VCR, but I'm pretty sure there are RCA to HDMI converters out there), there are a number of devices out there that'll take in HDMI and output class-compliant USB video (as though they're a webcam). That should work on Linux without too much cajoling.

Just going with hardware I've personally used, Elgato's got one (the Camlink 4K). Blackmagic Design actually has a few options; the ATEM Mini line all output video over USB, as will their Web Presenter.