Warning, if you are by chance related to me and have maybe asked me about these a couple of times and I have been less than helpful, these are already on their way to your house so don't buy them.
I tried a LOT of big-sibling books out on my firstborn while expecting my second. It was a natural fit--he loves books, I love books, we were all totally at sea as to what life would be like with two kids at home. My oldest was not quite two, and I didn't know how much was even possible for him to understand. And I wanted to prepare him without building The Event up into something that would worry him or shade his expectations the wrong way. I was a mess.
It probably says something that I haven't gotten around to writing this until now, but as we prepare for a new cousin, we've taken these books out again--and my eldest is suddenly explaining to me all about what babies like, what makes them happy, why they cry and what they might need. (He's three, but he is also an expert. Runs in the family.)
As it turns out, most of the new-baby-coming books were of no interest when there was no visible baby. It wasn't until life was different that he had much time for them. But then, these helped the most. And now, they're a delight to read, when it's a sweet thing to bond over instead of a source of anxiety.
Lola Reads to Leo is the best sibling book. It's not available as a board book, but I consistently love all the how-tos in this series, which are clear, accurate, loving, funny, and full of sweet details (see if you can figure out what beloved picture books Lola is reading from their impressionistic cover illustrations). This is a black mother, father, sister, baby brother family, and the mother nurses the baby.
Snuggle the Baby is the best indoctrination into baby care. It features cardboard pop-out pieces, flaps, and other novelty inclusions to help play with, feed, diaper, swaddle, and rock an adorable pop-out baby just about the right size for a toddler. The narration features examples of different feeding and soothing techniques on an array of big-eyed babies of many skin colors, with the cover baby called "my baby" and consistent throughout. (Also note that the colors on the Amazon page are significantly washed out compared to the print version; the baby has dark hair and dark eyes and the cover is blue.) I will say I have never figured out how that diaper thing is supposed to work; ours broke in the early, sleep-deprivedest days and is now a taped approximation.
My New Baby is less poetic but a wonderful conversation starter, with the child in the story prompting many of the questions any toddler will have about a new baby as the family goes through the tasks of the day. This family is a white hetero couple (nursing mother) with two children, neither signaling a gender. Waiting for Baby in the same series seems to have a different setup but I haven't seen it in person yet.
There are other lovely books about sibling relationships that continue past babyhood--for one, the picture book The New Small Person, which was a gift to us and is a total delight--but I think these three were the most useful for the initial landing. For anyone looking down this road, I send you a heartfelt "worth it" and wish you luck and simultaneous naps ASAP.