Once a conversation with a user is established, telegram bots can bleep away at you. Mine pings me whenever it puts a PR up, and when it's done responding to code reviews etc.

Right, but again that's not actually outbound at all, what you're describing is only inbound. Again, I thought the whole point was that the agent could start acting autonomously to some degree, not allow outbound kind of defeats the entire purpose, doesn't it?