My child loved Brambly Hedge at that age. He took it with him to summer camp and loved looking at all the illustrations when it was rest time.
https://a.co/d/dyiNuqm
Other suggestions
Dick King Smith books
Claude books (about a dog named Claude and his best friend Sir Bobblysock)
Roald Dahl books - there are several that are illustrated like James and the giant peach, the enormous crocodile
Michael morpurgo has some illustrated chapter books - he’s the war horse author
Jolly rogers books by Johnny duddle
I wouldn’t rush your child past picture books - I kept picture books for a long time and there is a lot of rich story telling there. Also sometimes kids just want a simple read just the same way that adults want to read people magazine and not the economist.