Based on what you shared, I think you need to add multiple Copy Data activities in your pipeline.
So, in this case, you need to configure each Copy Data activity to target your REST API endpoint (with each activity targeting different parts of your data if necessary).
Then for each Copy Data activity, in the Source settings, set up the pagination rule where you select AbsoluteUrl
and specify the absolute URL for pagination.
Then create a pipeline and add the multiple Copy Data activities created in the 1st step (where to dd multiple Copy Data activities)
You can use the parallel branching feature to execute these activities in parallel. Drag and drop each Copy Data activity in the pipeline editor to create parallel branches.