Like you I do not have a direct line with the diplomats of the involved countries, but every major news outlet was including Lebanon in the agreement.
What Israel is doing by itself is occupying more land and vilifying the concept of humanity, not "taking the south under control". Let me remind you that Hezbollah has founded as a direct reply to the '82 invasion of Lebanon by Israel.
The whole source of pain, misery and instability in the region is the colony of Israel, that was place there by the brits.
