Menu seems to be the kind of word that pops up in a lot of languages.

Some with extra letters, or accents, or fonts entirely. Other languages share the concept but the word is completely different.

μενού, valikko, roghchlár, メニュー , مِنو, меню́, trình đơn

To pick a few.

So translate it. Unless your app is so simple that it has no other text labels anywhere, you're going to need to need translations anyway.

Ideally, the translation needs to happen before the UI design. I've seen a lot of UI designs come straight from the designer with a beautiful pixel-perfect depiction of controls, but assuming English. So the "MENU" button was designed deliberately such that exactly four latin characters fit inside of it horizontally. Or assuming people's names fit in one line of text, or addresses have a certain number of lines and so on. Then when you get around to translating everything, the design has to go back to the drawing board.

> Great if you are an English speaker. Do we then translate that to every language we need to support?

Yes.

If the page isn't in the target language of the person using it, what difference does it make whether or not it says "menu" in English? If the user wouldn't be able to understand the contents of the menu, is it markedly better that they access those options via a hamburger icon vs an inscrutable bit of text?