@Translink Ua The cloud offering from Azure for translation is called Azure Translator. This is a cloud based translation service which offers different pricing tiers along with a free tier. You need to create a free Azure account to start using this resource or API for free upto the limits defined by the pricing tier chosen. Since the API is cloud based you can integrate the same with any 3rd party application/client as long as it supports REST API calls. I have referred the documentation of Trados and it does not look like this software has a readymade plugin to integrate Azure translator API.
I would recommend to try this service for free using any of the quickstarts to translate your content and check if it provides reasonable responses with various languages.
If an answer is helpful, please click on or upvote which might help other community members reading this thread.