what is the significance of the items to collect in this category?

I actually don't know myself. The category already existed when I became a mod here. ^^

core rivals was an event in early 2022 where twitch streamers competed in various challenges, eg. the battle of the bases referenced here:

https://twitter.com/CoreKeeperGame/status/1486021855043588103

i wasn't able to find a full list of events in the official discord or twitter, but, i suppose the scavenger hunt event was some kind of race/timed contest, which happened on some streams? haven't looked for footage.

if we have no runs it feels like a fairly arbitrary leaderboard today