I read cozy and historical mysteries, a bit of Paranormal/UF, and to mix it up, I read science and gardening books on occasion.
Not good news, I'm afraid, and everyone should definitely check out Themis-Athena's post for the most reliable work-around.
BUT, I've been playing around, trying to figure out why it's not recording the 2020 dates, and discovered that if you change your book status from your shelf, using the "shelves" column, to the "currently reading" shelf, it WILL add a 2020 start date (which you can see if you've configured your shelves to display the "start reading" column.
HOWEVER, any attempt to add a finish date - either through the "Finished Reading" button on the dash, or through the shelf page - breaks everything (ie, the start date disappears, along with no data in the End Reading column).
So, the date recording function works properly when the book is moved to Currently Reading, but anything done through the Shelf Advanced pop-up does not. I think someone forgot to define "2020" somewhere when they added the 2020 year to the pop up list (you'll notice it only goes to 2020, and I'm pretty sure last month it only went to 2019). This is actually easy to do, as some of you might remember we (ahem - *I*) did something very similar when the Festive Tasks form was first setup.
None of this is helpful to any of us at the moment, as I doubt any of us are keen to leave read books in our currently reading shelf for the sake of a date, but I'm posting this in case someone - ideally the person who did the 2020 alteration in the first place - will get the message and be able to more easily fix it.