I also think that secret chats are only available for smartphones, not for telegram app installed on computers.
Secret chats code can be verified since it's open-source, which is distributed as a part of TDLib and Telegram FOSS client available in F-Droid, however you have noted correctly that it's only available in mobile clients. Telegram Desktop had never published or released E2EE chats as a part of their client. There is a whole Github repo dedicated to that information and a discussion.
It's worth to highlight that the official mobile Telegram client from Google Play store is closed source and may have a modified implementation of Secret Chats that send encryption keys to their servers, therefore to ensure there is no malicious Secret Chats code, one should use the Telegram FOSS client from F-Droid.