Meaning no offense, it sounds like you're overthinking this.
The point of translation is not necessarily to go word-for-word. The point is to express the idea in the way it would have been expressed had the original writer been a native speaker of English (in this case). "New Year's Gala" is perfectly acceptable for this.
You could (optionally) choose to use a synonym like "Extravaganza", "Show", "Variety Show", or whatever, but it really doesn't matter much.
Trusting Google translate as the basis to make decisions about translation or translation quality is also not generally a very good idea. It's much better to get in touch with someone who's an actual (professional) live translator, and in this case, a native speaker of English. (Yes, I'm all of those things.)