MSE Brokers Cold Start Errors

Long initial class loading and networking times on the query path, for example Calcite class loading during compilation, can lead to errors if the first MSE queries received on the broker have tight timeout constraints (~1-2 seconds).

We can reliably reproduce these `Timed out while planning query` errors on the first few MSE queries, all with 1s timeouts, received on broker startup:
```
ERROR [PinotClientRequest] [jersey-server-managed-async-executor-9:210] Query processing exceptions: {400=BrokerTimeoutError: Timed out while planning query}
```

Start by reproducing the reported errors with the first few MSE queries received after broker startup, using the stated one-second timeout. Trace the query path through class loading, networking, and planning to identify the relevant entry points; done means those initial queries no longer fail with "Timed out while planning query" under the reported conditions.

Written by the indexing model from the issue text.