How to add a css class to postTitleWrapper in Gutenberg?

It’s probably related to how you’re loading that JS file, which causes it to run before the element is available (despite domReady).

You didn’t show how you’re loading the file etc, but your code works for me in a standard Gutenberg block edit.js:

export default function Edit() {
    domReady( function () {
        const postTitleWrapper = document.querySelector(
            '.edit-post-visual-editor__post-title-wrapper'
        );

        console.log( postTitleWrapper );

        if ( postTitleWrapper ) {
            postTitleWrapper.classList.add( 'something' );
        }
    } );

    return (
        <div>
            hello world
        </div>
    );
}

It also works in a Gutenberg plugin like this:

php

add_action( 'enqueue_block_editor_assets', 'enqueue_my_script' );

function enqueue_my_script() {
    wp_enqueue_script(
        'postTitleWrapperClass',
        trailingslashit( plugin_dir_url( __FILE__ ) ) . 'post-title-wrapper-class.js',
        array( 'wp-dom' ),
        filemtime( plugin_dir_path( __FILE__ ) . 'post-title-wrapper-class.js' ),
        true
    );
}

js

const PostTitleClassWrapper = () => {
    wp.domReady(function() {
        const postTitleWrapper = document.querySelector('.edit-post-visual-editor__post-title-wrapper');

        console.log(postTitleWrapper);

        if (postTitleWrapper) {
            postTitleWrapper.classList.add('something');
        }
    });
};

wp.plugins.registerPlugin( 'post-title-class-wrapper', {
    render: PostTitleClassWrapper,
    icon: null,
} );