When choosing the most appropriate localization platform, before obliging with Weblate, please consider if it supports different access levels for translators. Regular translators would contribute actually to the rough translation, while proofreaders (having more translation experiences, may also have permission to translate) can check the quality of the provided translations. When a localization is in quality assurance stage, regular translators may only suggest translations, when they find a better solution.
Another important criteria if the API of the chosen localization platform supported the automatic file conversion to the required JSON format. I recently translated for Sourcefabric on Transifex. After a certain interval of time the affected files were automatically updated in their GitHub repository.
As a result of this intention for centralization, a further step may be to connect to this translation repo during the installation process of ProcessWire and select and download the needed languages.
Regarding the documentation, why an external solution is needed? The Translate extension for MediaWiki enables you to translate the content into different languages. Install MediaWiki on a subdomain and start to work.