It seems like the issue you're encountering is related to the debugValue parameter being used instead of the actual value when calling dbutils.jobs.taskValues.get. This behavior is expected when the notebook is run outside of a job context, as the debugValue is returned in such cases
Please try this approach:
Task 1: Setting the value
dbutils.jobs.taskValues.set(key="batch_result", value="actual_value")
Task 2: Getting the value
value = dbutils.jobs.taskValues.get(taskKey="BatchProcessing", key="batch_result", default=None)
print(value) # This should print "actual_value" if running within a job context