Check if WorkRequest has been previously enquequed by WorkManager Android

Set some Tag to your PeriodicWorkRequest task:

    PeriodicWorkRequest work =
            new PeriodicWorkRequest.Builder(DataUpdateWorker.class, 15, TimeUnit.MINUTES)
                    .addTag(TAG)
                    .build();

Then check for tasks with the TAG before enqueue() work:

    WorkManager wm = WorkManager.getInstance();
    ListenableFuture<List<WorkStatus>> future = wm.getStatusesByTag(TAG);
    List<WorkStatus> list = future.get();
    // start only if no such tasks present
    if((list == null) || (list.size() == 0)){
        // shedule the task
        wm.enqueue(work);
    } else {
        // this periodic task has been previously scheduled
    }

But if you dont really need to know that it was previously scheduled or not, you could use:

    static final String TASK_ID = "data_update"; // some unique string id for the task
    PeriodicWorkRequest work =
            new PeriodicWorkRequest.Builder(DataUpdateWorker.class,
                    15, TimeUnit.MINUTES)
                    .build();

    WorkManager.getInstance().enqueueUniquePeriodicWork(TASK_ID,
                ExistingPeriodicWorkPolicy.KEEP, work);

ExistingPeriodicWorkPolicy.KEEP means that the task will be scheduled only once and then work periodically even after device reboot. In case you need to re-schedule the task (for example in case you need to change some parameters of the task), you will need to use ExistingPeriodicWorkPolicy.REPLACE here

You need to add a unique tag to every WorkRequest. Check Tagged work.

You can group your tasks logically by assigning a tag string to any WorkRequest object. For that you need to call WorkRequest.Builder.addTag()

Check below Android doc example:

OneTimeWorkRequest cacheCleanupTask =
    new OneTimeWorkRequest.Builder(MyCacheCleanupWorker.class)
.setConstraints(myConstraints)
.addTag("cleanup")
.build();

Same you can use for PeriodicWorkRequest

Then, You will get a list of all the WorkStatus for all tasks with that tag using WorkManager.getStatusesByTag().

Which gives you a LiveData list of WorkStatus for work tagged with a tag.

Then you can check status using WorkStatus as below:

       WorkStatus workStatus = listOfWorkStatuses.get(0);

        boolean finished = workStatus.getState().isFinished();
        if (!finished) {
            // Work InProgress
        } else {
            // Work Finished
        }

You can check below google example for more details. Here they added how to add a tag to WorkRequest and get status of work by tag :

https://github.com/googlecodelabs/android-workmanager

Edits Check below code and comment to how we can get WorkStatus by tag. And schedule our Work if WorkStatus results empty.

 // Check work status by TAG
    WorkManager.getInstance().getStatusesByTag("[TAG_STRING]").observe(this, listOfWorkStatuses -> {

        // Note that we will get single WorkStatus if any tag (here [TAG_STRING]) related Work exists

        // If there are no matching work statuses
        // then we make sure that periodic work request has been previously not scheduled
        if (listOfWorkStatuses == null || listOfWorkStatuses.isEmpty()) {
           // we can schedule our WorkRequest here
            PeriodicWorkRequest dataupdate = new PeriodicWorkRequest.Builder( DataUpdateWorker.class , 15 , TimeUnit.MINUTES)
                    .addTag("[TAG_STRING]")
                    .build();
            WorkManager.getInstance().enqueue(dataupdate);
            return;
        }

        WorkStatus workStatus = listOfWorkStatuses.get(0);
        boolean finished = workStatus.getState().isFinished();
        if (!finished) {
            // Work InProgress
        } else {
            // Work Finished
        }
    });

I have not tested code. Please provide your feedback for the same.

Hope this helps you.