refactor: split runAt request modules and harden broker flows

[ejgallego]

Summary

• split the standalone runAt plugin into request-oriented and shared support modules while keeping RunAt/Plugin.lean thin
• move reusable broker sync/save helpers into dedicated support modules and harden startup/request failure handling
• add focused regression coverage for request surface, handle lifecycle, and startup handshake behavior

Testing

• bash tests/test.sh
• bash tests/test-broker-fast.sh

Risks

• broad internal refactor across plugin and broker internals; wrapper-facing lean-deps surface churn from the stale Refactor runAt requests and harden broker flows #6 branch was intentionally left out of this replacement PR