With stream component we can record a live camera stream. But we cannot play it in Lovelace.
Well, I can now, sort of … but it involved writing a custom Lovelace card, a custom folder watcher component and a whole bunch of other shenanigans. And my Lovelace card looks crap since my JavaScript proficiency is zero and I just ended up using default html5 video player which seems to have intermittent caching issues.