Yes, I'm logged into the same CC account.
When I use the Adobe Stock website and save an image to a CC Library, the image doesn't not show up when I go into any of the Adobe apps (InDesign, Illustrator or Photoshop). Likewise, if I create a new CC library from the Adobe Stock site, said library doesn't appear in any Adobe app. However, all of the CC libraries that I've created inside of an Adobe app shows up on the Adobe Stock website. So, in summary, anything I do on the Adobe Stock website isn't reflected in the Adobe apps.
When I first started using Adobe Stock, I had similar syncing issues in InDesign. But, if I swapped over to Illustrator the image/library would sync, and then they'd show up in InDesign. This no longer works.
In my original post, I included a screen grab of my account on Adobe Stock. It's showing that I belong to two teams, even though I never set this up. So, I was wondering if these separate teams could be the cause of my issues, or if that shouldn't be an issue because regardless of what team I'm on, everything should sync in the apps regardless.
Please let me know if you require further explanation.