I’ve accidentally found a potential workaround solution - at least for my Pixelbook running CromeOS 92.0.4515.157 (Official Build) (64-bit)
When I download Plex from the Play Store, I don’t have the Download option (or the new Sync option). I haven’t had it for months.
However - if I download the latest available APK for armeabi-v7a from APKMirror Plex: Stream Free Movies & Watch Live TV Shows Now 8.21.2.27212 APK Download by Plex, Inc. - APKMirror it WORKS! and I can download/sync. Everything seems to work fine, but I haven’t really tried everything. But it can play and download (and play the download offline)
I think the Pixelbook is downloading the x86_64 version from the Play Store (which via the APK doesn’t work either) as I think it should. I don’t enough about the Android layer in this Pixelbook to know why the armeabi-v7a version works, but it does… at least for me.
I don’t have my Pixelbook in developer mode, so I had to go through these steps to be able to sideload the APK. It’s easy and took about 5 mins total How to Easily Sideload Android Apps on Chromebook [Guide] | Beebom
Your results may vary, but worth a shot. Total accident, I just downloaded the wrong file the first time…