In "Using custom builds of Godot" section, the book should provide instructions on how to update the automatically generated api.json file after upgrading the custom build.
I solved this problem by going to ~/.cargo/git/checkouts/godot-rust-1005fa777d499fc2/ and executing
find -name "api.json" -delete
After that, I removed the target folder in my Rust project to trigger a clean build from scratch. Not sure whether this is the best method. Please let me know if there's a better alternative.