The 500 Hats of Bartholomew Cubbins - Dr Seuss
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.
I really wanted to like Iggy Peck, Ada Twist, and Rosie Revere, because they promote really positive messages. But man, the verse is really clumsy and poor in some areas. Not stellar writing.
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
It didn't bother me that much, and there are some good rhymes. But if you want someone who takes meter seriously, check out Steven M Nedeau's books.