Just use a button

Is this actually true nowadays? Given that advice like this is often parrotted by people who don't actually use screen-reading software, I sometimes wonder if this is a situation where we've just been saying this and repeating this advice; meanwhile, screen readers have obviously become sophisticated enough to recognize that a div with an onclick handler on it is probably, you know, clickable and interactive.

Screen readers also don't access the DOM directly, there's an extra abstraction layer. Browsers expose accessibility data to the appropriate OS API, and screen readers use the data exposed by the OS. There's too much variation as-is between different screen readers to be piling browser-specific behavior on top.