fix(apigateway): StepFunctionsIntegration doesn't pass Cognito authorizer claims

### Describe the bug

When using `StepFunctionsIntegration` with a Cognito User Pool Authorizer and `authorizer: true` option, the Cognito claims are not properly passed to the Step Functions execution input. The VTL template iterates over `$context.authorizer.keySet()` but Cognito claims are nested under `$context.authorizer.claims`, resulting in an empty authorizer object.

### Regression Issue

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

### Last Known Working CDK Library Version

_No response_

### Expected Behavior

The Step Functions execution input should contain all Cognito claims inside the `authorizer` object:

```json
{
"authorizer": {
"sub": "user-id",
"email": "user@example.com",
"cognito:username": "username"
}
}
```

### Current Behavior

The authorizer object is empty or only contains top-level properties, missing the claims:

```json
{
"authorizer": {
"claims": ""
}
}
```

### Reproduction Steps

1. Create a Cognito User Pool
2. Create a RestApi with StepFunctionsIntegration
3. Configure the method with Cognito User Pool Authorizer
4. Set `authorizer: true` in the integration options
5. Deploy and invoke the API with a valid Cognito token
6. Observe that the Step Functions execution input has an empty authorizer object

### Possible Solution

The VTL template in `packages/aws-cdk-lib/aws-apigateway/lib/integrations/stepfunctions.vtl` (lines 53-62) needs to handle Cognito claims:

**Current code:**
```vtl
#if ($includeAuthorizer)
#set($inputString = "$inputString, @@authorizer@@:{")
#foreach($paramName in $context.authorizer.keySet())
#set($inputString = "$inputString @@$paramName@@: @@$util.escapeJavaScript($context.authorizer.get($
paramName))@@")
#if($foreach.hasNext)
#set($inputString = "$inputString,")
#end
#end
#set($inputString = "$inputString }")
#end
```

**Suggested fix:**
```vtl
#if ($includeAuthorizer)
#set($inputString = "$inputString, @@authorizer@@:{")
#if ($context.authorizer.claims)
#foreach($paramName in $context.authorizer.claims.keySet())
#set($inputString = "$inputString @@$paramName@@: @@$util.escapeJavaScript($
context.authorizer.claims.get($paramName))@@")
#if($foreach.hasNext)
#set($inputString = "$inputString,")
#end
#end
#else
#foreach($paramName in $context.authorizer.keySet())
#set($inputString = "$inputString @@$paramName@@: @@$util.escapeJavaScript($context.authorizer.get($
paramName))@@")
#if($foreach.hasNext)
#set($inputString = "$inputString,")
#end
#end
#end
#set($inputString = "$inputString }")
#end
```

### Additional Information/Context

_No response_

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

2.238.0

### AWS CDK CLI version

2.1105.0 (build 3e25a4e)

### Node.js Version

v24.12.0

### OS

Linux

### Language

TypeScript

### Language Version

5.9.3

### Other information

This issue is related to #30144 which was closed due to staleness. The problem still exists in the current version.

The fix should handle both Cognito User Pool Authorizers (claims in `$context.authorizer.claims`) and Lambda Authorizers (properties in `$context.authorizer`).

Start at packages/aws-cdk-lib/aws-apigateway/lib/integrations/stepfunctions.vtl and inspect the StepFunctionsIntegration authorizer template around lines 53-62. Reproduce the Cognito and Lambda authorizer cases described in the issue; done means Cognito claims appear inside the authorizer object while Lambda authorizer properties continue to work.

Written by the indexing model from the issue text.