WooCommerce which roles and capabilities control user login re-direct to Woo Account Page?

WooCommerce will only show the admin bar and give dashboard access to users who have the edit_posts or manage_woocommerce capabilities. If you don’t want to give users one of those capabilities, you can use the woocommerce_disable_admin_bar filter to give access and show the admin bar:

add_filter(
    'woocommerce_disable_admin_bar',
    function( $disable_admin_bar ) {
        if ( current_user_can( 'my_capability' ) ) {
            $disable_admin_bar = false;
        }

        return $disable_admin_bar;
    }
);

Despite the name that will also give access to the dashboard, in addition to showing the admin bar.

If you only want to give dashboard access without displaying the admin bar, you can use the woocommerce_prevent_admin_access filter, which works exactly the same way, or you can give the user/role the view_admin_dashboard capability.