You can run the CLI tool on Cloudron like https://docs.cloudron.io/apps/mattermost/#command-line-tool . Instead of the import command at https://docs.cloudron.io/apps/mattermost/#migration , use the export command.
To get a file off Cloudron, easiest way is to export to a path under /app/data and then use the File manager to download it.
I am also curious why you are not able to update mattermost on Cloudron. It's all automatic.