TLDR: Sites get a bonus container only accessible by Scouting survivors (plus luck). Details to be determined by balancing needs.
With the item-visibility bonus of Scouting now being available to all survivors once a building has been cleared, Scouting requires a supplemental bonus (per the livestream).
My proposal is to add a probability bonus for finding an extra searchable container once the survivor with Scouting finishes searching a site. When the final container is searched, survivors usually have an audio cue ("I've found everything I'm going to find here"). When a Scouting survivor completes the search of the last container, run the probability where 95% of the time (or whatever) the process runs as normal as described above but 5% of the time, a new container is activated and another audio cue sounds (One of the stock ones is fine: "Hmmm" or "Ah!"). I don't have strong feelings about whether the loot should be better than usual or by how much (I would lean towards good-ish loot). I'm also not sure if previously emptied sites should get a bonus container when entered (generally I would say no).