[BugFix] Harden distributed DP startup

[njhill]

Make distributed start up sequencing more robust:

• Have coordinator wait for subscription messages from all engines, then publish ready message
• Engines wait for this ready message before completing their handshake

[github-actions]

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[gemini-code-assist]

Code Review

This pull request aims to make the distributed startup sequence more robust by introducing a handshake between the coordinator and the engines. The changes look good and directly address the goal. I've identified two potential issues related to timeouts that could lead to hangs during startup. One is critical and could block the coordinator indefinitely, while the other is a high-severity issue that could cause the engine to wait forever for the coordinator. Addressing these will further harden the startup process.