What exactly is the deal with this ? idol / wooden statue?

Are you supposed to leave an offering of some kind, and check back later?

Is Balwan linked in some way to that empty hidden cache nearby?

You can find out more about it by talking to the couple that lives nearby.

If you have enough raw meat in inventory, you should get a special text option to leave an offering. This provides a one-time permanent benefit.

You'll find out pretty much straight away if it worked (I think it always does if the option is available)?

It's not linked to the hidden cache at all.

Thanks for that info.

Will try it out to see what happens.
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It worked. One extra point to the Luck Stat.

No problems.

Personally I was a tad disappointed it was luck and not something else more useful, but free stats are free stats.

Just a kind spoiler:

Do not write down a bad words on it before making the offering. If you do, well, you will regret. Trust me, I do.