You can change product content status in batch.

In simple version, published / unpublished is part of statuses

Note: Only for content with the same status

The steps are

With below interface

Pick relevant content

1. From content list, filter status ('Draft' in this example)

2. Check relevant content on left hand side

Set target status

3. Choose 'Update Status'

4. Choose 'Update Status'

5. Choose the target status (In this example, we change the status from 'Draft' to 'Pending Approval')

The batch job will be set in action.

Check update status

If everything goes smooth,

If there is any issue, you will need to download the file for status

An example of the error message