Thanks for the confirmation. The only thing that could be lost when signing out and back in to the app are annotations made or papers imported via the iPad after the sync issue started. All the information you’re able to see on Chrome is already safe in the cloud and wouldn’t be affected by this process.
If you find any of those recent PDFs are not showing up on Chrome and you wish to keep them, you can open them on the mobile viewer and share somewhere (like GDrive or via email) so you can then re-import them via web.
Another question - are you on the latest version of the app? This sync issue was supposed to be fixed with that release, so it would be helpful to know in which version it is occurring for you. You can check on the App Store - it should be 1.3.3. Let me know.