Currently, there is no way to identify the service desk project language using API's endpoints.
Include in the returned payload from the requests below a key with the language tag for the informed project.
https://developer.atlassian.com/cloud/jira/platform/rest/v2/api-group-projects/#api-rest-api-2-project-projectidorkey-get
or
https://developer.atlassian.com/cloud/jira/service-desk/rest/api-group-servicedesk/#api-rest-servicedeskapi-servicedesk-get