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.
Video capture:
1. there seems to be no capture device on the market that has a linux driver
2. some capture devices only provide their drivers on a CD/DVD
3. elgato video capture works (as long as the computer doing the capture is fast enough to process input in real time, otherwise the output is laggy)
Video processing (linux):
1. there's a bug in blender[1] that introduces audio skew to elgato-captured footage upon rendering. the skew is not there while editing
2. kdenlive[2] works fine with no audio skew
[1]: https://github.com/NixOS/nixpkgs/blob/6b74f99abd2f4c62e8093c...
[2]: https://github.com/NixOS/nixpkgs/blob/f6cd17269ea00766319388...