My attempts to copy a full collection to a group library I own are failing due to limited performance of my internet connection. My collection has more than 2000 items. Is it recommended to export the library in BibTex (or other) and re-import it to an empty group folder?
Exporting and importing is not recommended.
What exactly is the problem you're facing?
If dragging too many items at once isn't working, you can just drag in multiple batches.