[feature]: add ContextId and ContextName to child context logger

[zhongkechen]

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

Issue Link, if available

#80

Description

• lazy initialize logger
• use AutoClosable to clean up logger properties
• add context id and context name to context logger
• made the constructor of ExecutionManager accept DurableExecutionInput as the parameter.
• fixed suspension exception handling in child context operation

Demo/Screenshots

{
    "@timestamp": "2026-02-28T07:15:03.163Z",
    "ecs.version": "1.2.0",
    "log.level": "INFO",
    "message": "Order prepared, waiting for validation",
    "process.thread.name": "durable-exec-22",
    "log.logger": "software.amazon.lambda.durable.DurableContext",
    "contextId": "1",
    "contextName": "order-validation",
    "durableExecutionArn": "arn:aws:lambda:us-east-2:961306377283:function:child-context-example:$LATEST/durable-execution/79a965b4-f78f-4e04-895f-4bf4b1834bb9/4223b3d4-66d8-3c93-a74f-6bb112268f51",
    "requestId": "5392ff07-3dd5-4500-ba1c-7b87312c5e43"
}

Checklist

• I have filled out every section of the PR template
• I have thoroughly tested this change

Testing

Unit Tests

Have unit tests been written for these changes? Updated

Integration Tests

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Examples

Has a new example been added for the change? Verified