Hi Aurelien,
Yes you would use the asset api to get/put theme assets
https://shopify.dev/api/admin-rest/2023-01/resources/asset
you need the theme’s id and then you should be able to get it with:
/admin/api/2023-01/themes/[theme_id]/assets.json?asset[key]=config/settings_data.json
Cheers,
Gary