I'm not sure what "mini versions of the dump-cookies-temp-data" means, but the Cookies and Site Data section in the settings allows you to delete cookies, site data, and cache when Firefox is closed. You can specify website exceptions so they will not be affected when Firefox is closed.

Yes, I turn on temp file dumping with ever new instance of a browser. What I want to know is whether Mozilla has already or plans to eventually enable us to dump data after we close the last tab in a container while leaving the browser running with other containers still in use.

There is a Github issue filed about this, so Mozilla is definitely aware of it. (https://github.com/mozilla/multi-account-containers/issues/48) Unfortunately, it has been a long time since it was posted.