You can use <div role=button tabindex=0>.
Use a real <button>! You can style it.
This is a good article about Overriding Default Button Styles that also touches on why one should use a genuine <button>:
I’ve read so many of these, and it all comes down to a trade off which they decide goes a particular way but I don’t feel convinced by their reasoning. It still seems like, in cases where the appearance has to be pixel perfect you can either: add a few lines of accessibility code to a .button (which is consistently described every where I look), or add many many more lines of css reset code, which is quite opaque. The article you linked says that to reset the style... you end up applying -webkit-appearance:button. Whereas I thought the style reset would include removing that? Other sources online say that’s warranted.
There is a choice to be made, and the sort of “semantic-fundamentalism” preaching I see in these articles seems to be used as a way to avoid truly weighing up the options. They treat guidelines as laws and try to justify it from there. For me: it depends.
I don't understand why someone would want to add multiple attributes plus a JavaScript keypress listener to the wrong element when you can instead add basically reusable "reset" CSS to the right element (<button>).
You're making choices for the people using a site. If you use a <button> and don't get the CSS right, it doesn't always look the way you'd like for some people; if you don't use a <button> and an attribute or the JavaScript is wrong, it doesn't work at all for some people.
You don't have total control over the appearance of everything in the browser anyway. Some people want or need to make changes (higher contrast, more readable font, etc.) to use the web and not using appropriate elements just makes it harder for them to do that.
There are some scenarios where total control of the style is an important part of the thing being built.
I’m closing the browser now. I do appreciate the many constructive parts of what you’ve said. The preaching about what’s “wrong” I can skip. Like there’s some grand moral imperative not to connect a click handler to a div. Spare me!