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In simple version, published / unpublished is part of statuses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