How to migrate step machine to another account

You can use the DescribeStateMachine API to get the all the information about the state machine, including the definition and then use the CreateStateMachine to create a new one in the other account.

Hopefully you have used some Infrastructure as Code tool such as Cloudformation, SAM or CDK to create your Step Functions code. In that case you should be able to run the same IaC code by just modifying the parameters in another account.

If you have created manually on the AWS console, you can try copying the generated Amazon States Language (ASL) JSON code and create a new Step Function in the new account and paste the copied ASL after modifying relevant parameters. However, with this approach, the other resources such as Lambda functions, SQS queues, SNS topics etc. etc. that are being referred to by the Step Functions need to exist in the new account.