What is your end goal? Do you want to back up your videos with minimal storage costs? Compression won’t help you (because videos are already compressed) unless you can accept data loss through re-encoding. Handbrake (or pure ffmpeg) would be the tool to re-encode lots of files. This could save you space but you may have some loss of quality, depending on the configuration you use and how the original videos are encoded.
If you just want the videos to be available for streaming, tools like Jellyfin or Emby would do the job. They are servers that re-encode your media for streaming on the fly, depending on the client capabilities and your bandwidth settings.