Might work now. Did not test but found this in the docs:
Retrieving Storefront API translations:
You can query the supported resources using the Accept-Language HTTP header, to return translated content to the Storefront API.
I've tested this. The documentation seems to indicate that this should be possible, but it doesn't work.
Here is what I did:
But the content comes back in English. Has anyone else tried this and had more success?
After further investigation, I am pleased to report that this feature is working as described in the documentation here: https://shopify.dev/tutorials/manage-app-translations-with-admin-api#storefront-api-translation-head...
My mistake was to initially not use a sufficiently recent version of the Storefront API. This functionality works from version 2020-01 onwards.