A rather new addition to step functions can easily solve the problem with a single state; however it would most probably require converting each of the states of your current step function from JSONPath to JSONata format.

"Arguments": {
       "foo": "{% $exists($states.context.Execution.Input.foo) ? $states.context.Execution.Input.foo : 'bar' %}"
}

• You may use $states.input.foo rather than $states.context.Execution.Input.foo. However, the latter ensures it's the input you've received once the step function execution commenced and not a variable whose value could potentially have changed during the execution.

For further reading:

• Official AWS Developer Guides
  • https://docs.aws.amazon.com/step-functions/latest/dg/transforming-data.html
  • https://docs.aws.amazon.com/step-functions/latest/dg/workflow-variables.html
• JSONata Documentation - https://docs.jsonata.org/
  • Exists - https://docs.jsonata.org/boolean-functions#exists
  • Conditional Logic - https://docs.jsonata.org/programming#conditional-logic