can anyone recommend me good, battle-tested "slider" solution for playing videos as well as displaying images from single gallery? ideally capable of handling huge galleries (hundreds of items) with lazy loading

Not a today answer, but this is something I'm excited to build within the new Presets concept of video.js v10, where we can build specific "video interfaces" beyond a standard player using the composable architecture.

https://videojs.org/docs/framework/react/concepts/presets

I've used https://yet-another-react-lightbox.com/ in anger and it's great, very extensible too.