Brandon Sanderson has scheduled to publish The Stormlight Archivebook four in fall 2020, and no, he hasn't started to write this book yet! But no worries... Brandon is a determined writer who usually stays well on schedule :)
Brandon Sanderson: As you just read about above, I am on track for starting this book on January first. I’ll begin with a reread of the first three books, as I find I need a periodic refresher, even on my own novels. This will also be important for helping me really nail down the outlines for books four and five.
Note that while I’m optimistic about this being my fall 2020 release, delays could happen if the book doesn’t come out smoothly on the first draft. I’ll keep you updated with regular posts. A lot will depend on how long the revisions take.
Status: Book Four is my main project for 2019, for an anticipated 2020/2021 release.
More info can be found at Brandon's blog post.