One possible solution, if the machine has access to internet, is to install the Chrome extension with policy.
Starting with Studio 20.10, it should be automatically installed through policy if the conditions are met: internet access, admin rights, an enterprise licence of Studio.
For older versions of Studio or a community licence, the SetupExtensions tool can be used: About the SetupExtensions Tool
As for the cause of this issue, this needs careful investigation. Chrome can be launched with the command line flags
--enable-logging --v=1 and it will collect logs in a file
More info here: Chrome Browser debug logs - Google Chrome Enterprise Help
These command line flags can be passed in a workflow if Chrome is started with the
Open Application or the
Start Process activity.
It could be useful if the issue reproduces quickly. If it’s overnight then the logs could get very large.
Logs might reveal why the Chrome choses to disable the extention.