I got this reply from my contact at TikTok:
When TikTok Shop first launched, the ability to link multiple products was available. However, we found that it led to more GNE violations and fewer sales, so we decided to remove the feature.
New creators don't have access to it unless they received EC permission two years ago and have just started creating content now.
At this time, there isn't a way to grant new creators access to link multiple products, but I'll keep you updated if anything changes!