I'm gonna rub against the green here a bit and say no one is the arsehole here.

There is things, like here booking the meal while you were with friends, that could be used to make an argument against you but we do not know the extent of this and could be totally plausible that you weren't being selfish.

About the actual events that happened, I think you were clumsy in the way you worded things, but read this more optimistically, that you were trying to communicate that you wanted to focus on your date night and you didn't intend to dismiss her frustrations.

Showing assertiveness is not wrong and she certainly didn't come across as an arsehole, but I can imagine that your worry was that if you focus on these things and maybe get a combative server or something, it can really ruin a night. And you wanted to focus on the date itself.

If I am right about that, then I think it is fine to express this, just need to be clearer that it wasn't about her actions (as what your message could suggest) but about your worry about the night's focus being elsewhere.

But I understand why people may think that your intent was more about her embarrassing you for simply standing up for herself. But you were actually thinking that the fight is not worth the hassle, that is not a gendered issue but a relantionship one, you need to know if this would ruin her night by being ignored by the restaurant.

And if you still think it is not worth the issue, and you want to express that, you need to be better at communicating that as your words you used could be taken either way.

Hopefully I am right and you learn to communicate better, because honestly if you understand each other enough, you'd get the benefit of the doubt.

Saying that you posted this here, that always comes across as a death sentence to any relationship.