Unfortunately, I can’t tell you much about greek or peleponnesian agriculture, the focus was on chilling out (very recommendable place for this purpose!).
Just a few notes: Lots, really lots of olive trees. The Kalamata area that includes parts of Mani is Greece’s main olive oil production zone.
There were hardly any sheep or cows around, so I assume, that the milk production is not important on Mani, not surprisingly, it’s very dry here and rather hard to feed cows. Those here were pretty much on their own. The second time we saw them, they were on the way home, unaccompanied.
Except for some bigger olive oil operations, farming is predominantly small scale. But most of the olive farmers are to small for big presence on the markets. The austrian Company Bläuel hat taken this niche and collects oil from different producers which is then exported, eg. to Migros in Switzerland.