Would be interesting to know what Iran actually communicated to...

Would be interesting to know what Iran actually communicated to the US through Swiss embassy and Oman. Rumors are circulating that it offered to not directly respond to Israel, if US brokers a permanent ceasefire in Gaza. I personally doubt that. But if true, it let's Biden save his election campaign from inflation and another ME war, Iran gets to avoid a costly confrontation with Israel, and Gaza get a chance to survive this humanitarian crisis. That would be a very desirable outcome for almost everyone.

Could explain recent Biden's pressure on Israel and today's withdrawal of some Israeli troops from Gaza.

But like I said I personally doubt that, given Netanyahu has likely considered all these scenarios when he played the Iran-escalation card. A deal like that will effectively throw him under the bus, at a time he is facing significant internal challenges.