If you want to develop your own application / monitor web page, you can look at the interface JobExploreror JobOperator. It provides you methods for getting JobExecutions, and in JobExecutions you can get StepExecutions. All this gives you job status and individual steps inside.
Change response for comment:
Spring Batch. . . , . ( , , - , Spring Batch), tasklet Spring . ( : , execute(), FINISHED , , ..).
, , , JobExplorer JobOperator, → → .