Register new region: ap-south-2

🚀 Checklist:

- [x] Add region in [AWS_CDK_METADATA](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L1) (commented out).
- [x] Add region and zone id in [ROUTE_53_BUCKET_WEBSITE_ZONE_IDS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L40).
- [ ] Add region and zone id in [EBS_ENV_ENDPOINT_HOSTED_ZONE_IDS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L77).
- [ ] Add region and account in [ELBV2_ACCOUNTS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L116).
- [x] Add region and account in [DLC_REPOSITORY_ACCOUNTS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L149).
- [ ] Add region and account in [APPMESH_ECR_ACCOUNTS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L174).
- [x] Add region and ARN in [CLOUDWATCH_LAMBDA_INSIGHTS_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L202) for 1.0.178.0.
- [x] Add region and CIDR block address in [FIREHOSE_CIDR_BLOCKS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L498).
- [x] Add region and ARN in [ADOT_LAMBDA_LAYER_JAVA_SDK_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L529) for most recent version in x86_64 and arm64.
- [x] Add region and ARN in [ADOT_LAMBDA_LAYER_JAVA_AUTO_INSTRUMENTATION_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L608) for most recent version in x86_64 and arm64.
- [x] Add region and ARN in [ADOT_LAMBDA_LAYER_JAVASCRIPT_SDK_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L689) for most recent version in x86_64 and arm64.
- [x] Add region and ARN in [ADOT_LAMBDA_LAYER_PYTHON_SDK_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L768) for most recent version in x86_64 and arm64.
- [x] Add region and ARN in [ADOT_LAMBDA_LAYER_GENERIC_ARNS](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/build-tools/fact-tables.ts#L847) for most recent version in x86_64 and arm64.
- [x] Add region in [AWS_REGIONS_AND_RULES](https://github.com/aws/aws-cdk/blob/v2.65.0/packages/@aws-cdk/region-info/lib/aws-entities.ts).
- [ ] Run integ tests and update snapshots

Review the unchecked entries in packages/@aws-cdk/region-info/build-tools/fact-tables.ts, then verify the ap-south-2 entry in packages/@aws-cdk/region-info/lib/aws-entities.ts. Run the integration tests and update the snapshots as requested; done means all checklist items are complete and the tests pass.

Written by the indexing model from the issue text.