It provides pretty good translations, but it's not particularly good for privacy. Obviously it's better than Google, but their privacy policy isn't great.
My main issue is they want credit card info to get an API key, which is required if you want to use it through (properly integrated) addons or whatever. The translations are pretty much magic though. Really good results most of the time.
Translate You features LibreTranslate, Lingva, DeepL, MyMemory, Reverso, and SimplyTranslate.
While I can't speak for any of them, I think that all of those should be safe being that Translate You is FOSS, and their idealogy is "No Ads, no trackers, just You"
The SimplyTranslate front end has many languages, translate engines selectable: Google | DeepL (Testing) | ICIBA | Reverso | LibreTranslate. Some instances are Tor-friendly, even onion. The project page seems to be https://codeberg.org/SimpleWeb/SimplyTranslate
Refusing to use Google is just common sense. LibreTranslate itself is decent (at least not Google), except a website hosting it may have some opaque JS or Google things (Font, Analytics, TagManagers, etc.)
Either way, translation can’t be super-private in general. For example, if you use it to write a private message or love letter in a foreign language… even including real names and physical addresses…
Also, metadata like “a Danish-speaker is reading this German text about X” can’t be hidden, and if the language pair is uncommon and/or if text to be translated is specialized (not generic), the engine provider may easily guess “this request and that request yesterday may be from the same user”, etc. if they want to. A sufficiently powerful “attacker” might de-anonymize you, helped by other info about you, already gathered. In practice, maybe not a big concern, if you’re just translating generic, non-sensitive text, not showing your real IP, and clearing cookies frequently.