According to the navbox, Translate uses the following tables:
None of these are available in Wikimedia’s public replicas (e.g. through Quarry). The mediawiki.org documentation of these tables doesn’t contain anything other than the schema, so I don’t know whether they contain private data, but I guess at least most of them don’t. Can you please evaluate them and make public as many as possible? Especially revtag would be important, as it’s (AFAIK) impossible to query for translatable pages without it, but others may also be useful for the general public. One of Wikimedia’s core values is openness, so the default should be that DB tables are available in public replicas unless there are strong reasons against it, not that they aren’t available unless there are strong reasons to make them public.