Code Modernization: Fix 'ping_sites' non-nullable deprecation.

When saving options from the Settings page, include the `'ping_sites'` option in the allowed "writing" options list only when the `'blog_public'` option is `'1'`.

Fixes a PHP 8.1 and above "null to non-nullable" deprecation notice in `sanitize_option()` ([https://core.trac.wordpress.org/browser/trunk/src/wp-includes/formatting.php?annotate=blame#L4952 which happens when here] as part of [22255]):

{{{
Deprecated: explode(): Passing null to parameter #2 ($string) of type string is deprecated in .../wp-includes/formatting.php
}}}

**Explanation**

[https://developer.wordpress.org/apis/options/#writing Per the documentation], the `ping_sites` option requires the `'blog_public'` option to have a value of `'1'` and must be a `string` data type. `null` is not valid for this option.

The relationship between the 2 options shows itself in the `options-writing.php` code ([https://core.trac.wordpress.org/browser/tags/6.5.4/src/wp-admin/options-writing.php#L233 shown here] and in [4326]), as the `textarea#ping_sites` only renders when `'1' === get_option( 'blog_public' )`.

**What happens if `'blog_public'` is not `'1'`?**

The `'ping_sites'` option will not be a field on the page. Upon saving:

* HTTP POST (`$_POST`) does not include `'ping_sites'`. 
* Before this commit:
   * The [https://core.trac.wordpress.org/browser/trunk/src/wp-admin/options.php#L333 option's value was set to] `null` before being passed to `update_option()`. 
   * `update_option()` invokes `sanitize_option()`.
   * A `null` value for the `'ping_sites'` case was passed to `explode()`, which threw a deprecation notice on PHP 8.1 and above.
* With this commit, the `'ping_sites'` option is no longer included in the allow list and thus will not be passed to `update_options()` > `sanitize_option()` > `explode()`.

Follow-up to [22255], [12825], [4326], [949].

Props kitchin, SergeyBiryukov, swissspidy, devmuhib, rajinsharwar, hellofromTonya.
Fixes #59818.

git-svn-id: https://develop.svn.wordpress.org/trunk@58425 602fd350-edb4-49c9-b593-d223f7449a82

src/wp-admin/options.php

@@ -181,7 +181,9 @@
 	$allowed_options['general'][] = 'default_role';
 
 	$allowed_options['writing']   = array_merge( $allowed_options['writing'], $mail_options );
-	$allowed_options['writing'][] = 'ping_sites';
+	if ( '1' === get_option( 'blog_public' ) ) {
+		$allowed_options['writing'][] = 'ping_sites';
+	}
 
 	$allowed_options['media'][] = 'uploads_use_yearmonth_folders';