https://api.getlocalization.com/[project]/api/translations/list/json/ API let's you fetch current status of your translations for each language. It returns progress and review_progress values.
Here are the details what these values mean:
progress indicates how many percentages the specific language is translated.
review_progress indicates how many percentages of your currently translated content is approved. This is meaningful if your "Minimum acceptance level for translations" in your project setting is set for something else than "Accept all translations".
If you want to check whether your project is fully translated AND approved, you should check that both of these values are 100%. Just relying on review_progress to check whether everything is translated and approved is not enough.