Harry the Dirty Dog series
Amelia Bedelia series
Little Toot
Katy and the Big Snow
Tikki Tikki Tembo
Eloise
Babar series
Others from Weekly Reader - including Gus was a Friendly Ghost, Be Nice to Spiders, The Mystery of the Great Swamp, and Mike Mulligan and his Steam Shovel
Later
Stuart Little series
Probably rare because the young protagonist who over-judges the severity of his minor problem, gulliblly starts on a quest where he increasingly suffers worse, finally concludes the actual solution is to confront his problems with swift and blinding violence. I read it so many times I can still recall a good portion from memory.
My personal favourite was "Stig of the Dump", which still holds up today, unlike many from my childhood.
The Monster at the End of this Book
The Little Red Caboose
Favorites to Read to Kids:
The Hiccupotamus
Dear Zoo
The Sneetches
Mercy Watson to the Rescue
Pete the Cat (I Love My White Shoes or His Four Groovy Buttons)
Favorite Authors: Mo Willems, Sandra Boynton
If You Give a Mouse a Cookie - the original is by far the best of these.
Ramona Quimby series - Beverly Cleary
Iggy Peck, Architect (+series) - Andrea Beaty
Beast Feast - Emma Yarlett
Dragons Love Tacos (+ 2) - Adam Rubin
The Princess in Black (+series) - Shannon & Dean Hale
Don't Let a Unicorn Scribble (+series) - Diane Abler
The Camping Trip - Jennifer Maan
Maddie & Mabel (+series) - Kari Allen
I Love You Stinky Face - Lisa McCourt
Authors that were always good: Arnold Lobel, Sandra Boynton, James Stevenson
And don't forget to check https://www.betterworldbooks.com/ , they are affiliated with the Internet Archive and they don't show up in shopping searches.
To add to your list: anything by Julia Donaldson. The Gruffalo, Super Worm, Room on the Broom, the Whale and the Snail.
Perennial favs when my kids were 3-5
The Mouse and His Child - Russell Hoban
A Wizard of Earthsea: A Graphic Novel - Ursula K. Le Guin, Fred Fordham
The SAS Survival Handbook - Lofty Wiseman
They more or less all cover the search for being self winding.
The only one I didn't have is Yertle The Turtle
The Skull (Jon Klassen)
The Way Things Work (David Macaulay)
Animalia (Graeme Base)
Nanette’s Baguette (Mo Willlems)
The princess and the Pony (Kate Beaton)
Frederick (Leo Leoni)