A simple Lightroom-based workflow is to separate videos logically, not necessarily physically, at first.

In Lightroom Classic, create a Smart Collection with File Type = Video (older wording may be Media Type = Video). That gives you an always-updated view of only your video files, while keeping them in context with the original shoots.

If you want a fully separate video workflow, one community-tested option is to right-click that Smart Collection and export it as a catalog. Lightroom Classic can copy those video files into the new catalog while preserving the existing folder hierarchy, so you can open that catalog when working only on video.

If you actually want to move video files into a different folder structure on disk, a command-line tool like exiftool can do that based on dates and file types, but it takes more care and setup.

As for why Lightroom imports video: Lightroom has supported basic video handling for years, including organizing and some simple processing, so it isn’t limited strictly to still photos.