You need to deserialize, modify, and re-save the item.
Remember that localStorage is a simple key/value store for strings: it does not provide any way to manipulate the contents of those stored strings (you don't even need to store JSON, you could store YAML, XML, or Base64-encoded arbitrary binary data in localStorage.
Like so:
function storeCart( cart ) {
    
    localStorage.setItem( 'cart', JSON.stringify( cart ) );
}
/** Returns 'true' if the specified key/value was removed from the stored cart object - otherwise 'false'. */
function deleteItemFromStoredCart( key ) {
    
    const cartString = localStorage.getItem( 'cart' );
    if( !cartString ) return false;
    
    try {
        const cart = JSON.parse( cartString );
        if( !( key in cart ) ) return false;
        delete cart[ key ];
        storeCart( cart );
        return true;
    }
    catch( err ) {
        console.log( "Error: ", err );
        return false;
    }
}