Not sure if they're explicitly sharing data, but there does seem to be something that's sharing data across the platforms. When I buy something from Tiktok, the ads for the same thing shows up on my instagram almost instantly. Doesn't necessarily mean they're directly sharing data of course, could be a third party too. But as a consumer that has very little difference for me.
It's because you are the exact target demographic consumer for that product, and it's visible in your behavior patterns when using your apps combined with what they know about you (age, sex, location, demographics, etc.)
If you buy something from Tiktok, you presumably visit the merchant's website, which almost surely will have chosen to have a tracking pixel that sends data to FB (Instagram). You can read a bit about how tracking pixels work here: https://jvns.ca/blog/how-tracking-pixels-work/
In this case it's not Tiktok and Instagram that are sharing data with each other, but the product website that is choosing to share data with both of them.