Obtaining a W-2 from a previous employer

by law they're not required to issue them before 1/31/2020. so you might not get it until sometime in February.  

"Shouldn’t they know to mail it to me automatically without my intervention? Is that practical HR accounting to include previous employees who’ve moved on?"

If they are competent, then they should mail you a W-2 regardless of whether you worked one day, one week, one month, or whatever.  If your address has changed, you need to notify the former employer.