They use Google Translate informally and for free.
Before the New Year, Telegram added a function for translating messages from a foreign language (which, however, did not work smoothly for everyone). Developer Daniil Petrov found out that the messenger team is using the unofficial Google Translate API.
It is reported that on iOS, messages are translated through the “System Translation” feature. For Android, the Telegram developers decided to use the unofficial Google Translate API. It allows you to send translation requests as if they were sent by the standard Google Chrome site translation feature. These requests can be “presented” by different browsers to avoid blocking.
So Telegram translates a large number of messages without paying for the official Google Translate API. That is, the messenger was able to save money. So far, Telegram itself has not commented on this in any way.