Disable for WooCommerce Store Manager

Do you mean the Shop Manager role? I’m not too familiar with WooCommerce, but anyone without the manage_options capability should not be able to access the Code Snippets menu.

If you need to change what capability this is, you can do so like this:

add_filter( 'code_snippets_cap', function ( $cap ) {
    return 'manage_woocommerce';
} );