I have tried to reproduce in both Publishing site collection and other site collections but turning out that the Approval Status of Document Set can't be influenced by the Approval Status of uploaded document.
For a better troubleshooting, I suggest to do as below:
1. Do the same operation on other sites to check whether it's a site template issue.
2. Do the same operation on different Document Library to see whether it's a document library issue.
Microsoft is conducting an online survey to understand your opinion of the Technet Web site. If you choose to participate, the online survey will be presented to you when you leave the Technet Web site.