Support Lambda Durable Functions

[fossamagna]

Environment information

System:
  OS: Linux 6.6 Debian GNU/Linux 11 (bullseye) 11 (bullseye)
  CPU: (8) arm64 unknown
  Memory: 18.94 GB / 23.43 GB
  Shell: /bin/bash
Binaries:
  Node: 22.16.0 - /usr/local/bin/node
  Yarn: 1.22.22 - /usr/local/bin/yarn
  npm: 10.9.2 - /usr/local/bin/npm
  pnpm: undefined - undefined
NPM Packages:
  @aws-amplify/auth-construct: 1.8.1
  @aws-amplify/backend: 1.16.1
  @aws-amplify/backend-ai: Not Found
  @aws-amplify/backend-auth: 1.7.1
  @aws-amplify/backend-cli: 1.8.0
  @aws-amplify/backend-data: 1.6.1
  @aws-amplify/backend-deployer: 2.1.3
  @aws-amplify/backend-function: 1.14.1
  @aws-amplify/backend-output-storage: 1.3.1
  @aws-amplify/backend-secret: 1.4.0
  @aws-amplify/backend-storage: 1.4.1
  @aws-amplify/cli-core: 2.2.1
  @aws-amplify/client-config: 1.8.0
  @aws-amplify/data-construct: 1.16.3
  @aws-amplify/data-schema: 1.21.0
  @aws-amplify/deployed-backend-client: 1.8.0
  @aws-amplify/form-generator: 1.2.1
  @aws-amplify/model-generator: 1.2.0
  @aws-amplify/platform-core: 1.10.0
  @aws-amplify/plugin-types: 1.11.0
  @aws-amplify/sandbox: 2.1.2
  @aws-amplify/schema-generator: 1.4.0
  @aws-cdk/toolkit-lib: 1.1.1
  aws-amplify: 6.15.3
  aws-cdk-lib: 2.189.1
  typescript: 5.8.3
No AWS environment variables
No CDK environment variables

Describe the feature

Support configure for Lambda Durable Functions in defineFunction.

Use case

long time tasks without custom CDK construct. (ex: invoke from a scheduler, etc)

Alternatives:

• Configure a Step Functions StateMachine using a CDK Construct
• Use the custom function feature. Note that some features like Amplify secrets and environment variables are unavailable in this case.