Where does Jetbrains Gateway store plugins?

Our team currently uses docker containers for rust development.  Most of the team successfully manages day to day development with vs-code by attaching vscode directly to the container.  However, I would like to use clion for this setup, as I have a lot of experience with Intellij products in my workflows.

I can't use the docker attach capabilities in Intellij due to the Rust plugin not being compatible (seems to rely on local rust toolchain and not the one inside the container).  My idea was to use Jetbrains Gateway via ssh into the container.

This works relatively well with one significant issue, plugins on the host (container) get blown away every time I restart the container.  I currently have the directory that contains all the source code *and* ~/.cache/Jetbrains mounted into the docker container.  This successfully allows me to persist a bunch of cache (and not have to redownload the IDE every time) but this *does not* persist plugins.

According to other docs I could find, plugins are usually stored in ~/.local/JetBrains, but this directory is empty after installing plugins on the host.  The official Jetbrains Gateway docs claim that plugins are stored on a per project basis, but does not expand on where that storage is done (it's not with source code as far as I can tell).  

So where does Gateway store host plugins so I can persist them, and not have to manually re-install them every time?