the application's data path can be found at /home/yellowtent/appsdata/<appId>/data/ and that is the only writeable path for apps (besides /tmp and /run of course). This is done for security as well as predictability for updates. Usually if you push data there through external means like SSH, you might have to reconfigure the app through the dashboard, in case the file permissions are not correct. Generally it is preferred that data changes are done via the app itself, which I guess is not quite applicable for your use-case though.
For duplicator, from what I understand this migration script is mostly just creating a tarball/zipfile of the whole previous installation and then extracts it into a folder, which is served up by some LAMP environment. This is incompatible with the Cloudron WordPress package, for reasons mentioned above (mostly the read-only fashion) For this you probably have to fallback to the LAMP app itself. There it should work.