In the book "careless people" it is highlighted that Facebook embedded spyware in their app which tracked other apps that were installed/used on the phone. This allowed them to figure out that so many of their users were installing WhatsApp, and enabled the legendary WhatsApp purchase. It is very much possible that Instagram is reading some sort of temporary files created by TikTok and extracts data using this method.

Facebook/Meta has a proven track record of fetching all data from your phone, even when abusing security vulnerabilities to do so. And the clowns at Apple can't even fix RCEs in their network-exposed applications, I'm not convinced the separation between apps is flawless.