(aws-stepfunctions): `DistributedMap` prop `resultWriter` doesn't work when integrating with StateMachine

### Describe the bug

`DistributedMap` prop `resultWriter` seems like never works with StateMachine, while `resultWriterV2` does.

### Regression Issue

- [ ] Select this option if this issue appears to be a regression.

### Last Known Working CDK Library Version

_No response_

### Expected Behavior

`resultWriter` prop should be deprecated or at least works for old features.

### Current Behavior

When using `resultWriter` with StateMachine, SM's DefinitionString doesn't have any `ResultWriter`.

### Reproduction Steps

Check this integration https://github.com/aws/aws-cdk/blob/2cdfc8a909ce3752833e46dd2ed0106fee0e785a/packages/%40aws-cdk-testing/framework-integ/test/aws-stepfunctions/test/integ.distribution-map-with-result-writer-jsonata.ts#L26-L29

Its snapshot template confirms the issue, DefinitionString doesn't have any `ResultWriter`, https://github.com/aws/aws-cdk/blob/2cdfc8a909ce3752833e46dd2ed0106fee0e785a/packages/%40aws-cdk-testing/framework-integ/test/aws-stepfunctions/test/integ.distribution-map-with-result-writer-jsonata.js.snapshot/aws-stepfunctions-map-with-result-writer.template.json#L201-L216

Run the integration `yarn integ test/aws-stepfunctions/test/integ.distribution-map-with-result-writer-jsonata.js --force --no-clean`, we will see nothing is output to the result bucket.

### Possible Solution

Deprecate `resultWriter` prop as `resultWriterV2` works fine. As we already deprecated `ResultWriter` class, I think we should do the same for the prop.

### Additional Information/Context

_No response_

### AWS CDK Library version (aws-cdk-lib)

main

### AWS CDK CLI version

all

### Node.js Version

all

### OS

all

### Language

TypeScript

### Language Version

_No response_

### Other information

_No response_

Start with the integration in test/aws-stepfunctions/test/integ.distribution-map-with-result-writer-jsonata.ts and compare its generated DefinitionString with the snapshot at test/aws-stepfunctions/test/integ.distribution-map-with-result-writer-jsonata.js.snapshot/aws-stepfunctions-map-with-result-writer.template.json. Run the documented integration command to reproduce the missing ResultWriter output. Done means the resultWriter behavior is corrected or the prop is explicitly deprecated, with the integration output and snapshot reflecting the chosen behavior.

Written by the indexing model from the issue text.