Adding custom URLs to the sitemap does not respect “Links Per Sitemap”

Hello, as the title suggests, I’m finding that adding custom URLs to the sitemap does not respect the “Links Per Sitemap” setting.

I followed the guidance from here in order to create a filter that adds additional URLs to the sitemap from a custom database table.

It works just fine after regenerating the sitemap, however, the primary issue is that all of the URLs are added to the sitemap without any pagination. So I have well over 200 items on a single sitemap. Is there a way to add these items while ensuring that the sitemap is broken up into separate pages so I can follow best practices? Thank you!

Note: Here is an example of my filter.

function rank_math_add_custom_urls(): string
{
        $urls = '';
        $site_url = get_site_url();
        foreach(CustomMysql_Util::get_custom_sitemap_links() as $result) {
            $url = "$site_url" . "$result->uri";
            $lastmod = "$result->lastmod";
            $value = "<url>
                <loc>$url</loc>
                <lastmod>$lastmod</lastmod>
            </url>";
            $urls .= $value;
        }
        return $urls;
}
add_action( 'rank_math/sitemap/page_content', 'rank_math_add_custom_urls', 10 );