I have exactly the same problem. The file browser for the selections of addons does not work. It is neither possible to click on a file nor to move. I had the same problem with a previous installation, but there it somehow worked after some restarts.
This would be some problem with the Chromebook configuration or, if you're using a third-party Zotero package, restrictions of the package (e.g., sandboxing). Zotero just tries to open a standard OS filepicker.
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https://www.zotero.org/support/reporting_problems#provide_steps_to_reproduce