[Lambda] Support for a Function Shutdown lifecycle phase

Start with the AWS Lambda runtime-environment documentation and compare the documented INIT and SHUTDOWN phases. Review the aws-samples/graceful-shutdown-with-aws-lambda workaround and the note that Lambda extensions can participate in shutdown. Done means the roadmap request has a defined, officially supported path for function cleanup, with updated documentation and no required extension workaround.

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Tell us about your request
Lambda Functions currently have support for a Function Init step as part of the INIT phase as outlined here

This step is most commonly used for establishing connections to other resources such as Databases

However, there is no equivalent Function Shutdown step as part of the SHUTDOWN phase.
This could be used to add symmetry to Init where database connections can be closed.

Which service(s) is this request for?
AWS Lambda

Tell us about the problem you're trying to solve. What are you trying to do, and why is it hard?
We want to be able to manage our database connections in a cleaner manner. Currently Lambdas can open database connections on Init, but we have no clean way of closing the connection.

Either we open and close the connection as part of the request, or, we leave the connection open and wait for the server to close it after it is marked as idle.

This creates connection management issues with servers where there appears to be a larger number of in-use connections than there really are.

Allowing the Lambda code to participate in the Shutdown phase would allow the function to clean up after itself and better manage system resources.

Are you currently working around this issue?
We carefully manage various client connection settings such as idle timeouts, and live with the fact that our number of open connections is often not completely representative of active connections.

Additional context
Lambda extensions are able to participate in Shutdown, it appears that it is just function code that cannot officially do that.

However, there are documented workarounds such as those found in aws-samples/graceful-shutdown-with-aws-lambda. So it doesn't feel like a stretch to make this an officially supported behaviour with more explicit documentation and no requirement for an extension to first be added.

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