You can fetch https://meta.wikimedia.org/w/api.php?action=query&meta=messagegroupstats&mgsgroup=page-Library%20Card%20platform and filter out the languages with 0 translations (there should probably be a built-in flag to do that), although you'd have to know that fragments of a translated page are in the page-<pagename> message group (and that message groups are a thing) so yeah, not great. (Also why do I get a deprecation warning about mgstimelimit even though it's not used?)

In T215456#4933630, @Tgr wrote:

(Also why do I get a deprecation warning about mgstimelimit even though it's not used?)

Core API bug, it doesn't account for deprecated parameters that have default values. Filed T215548.

@Reedy Does the meta=messagegroupstats API satisfy your use case?

In T215456#4975442, @Nikerabbit wrote:

@Reedy Does the meta=messagegroupstats API satisfy your use case?

It's not my use case, it was a re-post of a question on irc... :)

I'm not sure what to do without additional feedback.

I asked the question and I think there should be a simpler and more straightforward way of retrieving the translated languages of a particular page.

In T215456#4975489, @AVasanth_WMF wrote:

I asked the question and I think there should be a simpler and more straightforward way of retrieving the translated languages of a particular page.

I'd agree; as is often the case, it's partially Documentation and T2001: [DO NOT USE] Documentation is out of date, incomplete (tracking) [superseded by #Documentation]

It's certainly not obvious from https://meta.wikimedia.org/w/api.php?action=help&modules=query%2Bmessagegroupstats how I would get the list of translations for a page