I bought a Sony NEX-7 camera, mainly for testing purposes but it will now become my main camera for taking photos.

However, the menu is entirely in Japanese and there is no language option.

I am aware that some people were looking into making a kind of patch for this situation but I can't find much information and definitely nothing that seems to be working. Does anyone have more information on this?

In your research did you run across this:

It is possible!

From the (english language) manual, page 25:

There is a little icon, a small black box with the letter A on it, kind of looks like a tiny character sized picture of a book.

Go into the settings menu, the toolbox icon, and scroll down until you find this the letter A icon, select and there you have all your languages,

Good luck!

Source https://community.sony.com/t5/Customer-Relations/NEX-7-menu-language-cannot-be-changed-from-Japanese-to-other/td-p/240337

Sadly this is a NEX-7 purchased in Japan, so it doesn't have the language menu.

I found one website that sort of edits the camera but they went only as far as the NEX-6 in doing so. Apparently all those cameras use android "apps", but not the NEX-7 (and possibly onwards).