max

this htaccess can perhaps be improved upon somewhat (eg. less ‘footprint’ from wildcard matches and value captures) in this use case as follows:

www to non-www

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} ^www\.(.*)$ [NC]
RewriteRule ^ https://%1%{REQUEST_URI} [R=301,L]

non-www to www

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} !^www\.(.*)$ [NC]
RewriteRule ^ https://www.%1%{REQUEST_URI} [R=301,L]

and ONLY if using 100% HTTPS

www to non-www

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} ^www\.(.*)$ [NC]
RewriteRule ^ https://%1%{REQUEST_URI} [R=301,L,S=1]
RewriteCond %{HTTPS} !=on
RewriteRule ^ https://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]

non-www to www

RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} !^www\.(.*)$ [NC]
RewriteRule ^ https://www.%1%{REQUEST_URI} [R=301,L,S=1]
RewriteCond %{HTTPS} !=on
RewriteRule ^ https://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]

Error messages can be both confusing and misleading.

Since you note that you have quite heavy traffic, perhaps you can increase the open-files-limit to more than 10,000 ??

Indeed! FOr the OP and any future readers:

The process to increase open_files_limit is different depending upon your OS…
https://duntuk.com/how-raise-ulimit-open-files-and-mysql-openfileslimit (centos 6, and likely earlier)
https://ma.ttias.be/increase-open-files-limit-in-mariadb-on-centos-7-with-systemd/

Google is your friend… so is dba.stackexchange.com and https://community.spiceworks.com/databases and the like… hope you got your issue resolved =)

You can try using an mu-plugin (all thanks to Sybre!)

<?php
/*
 * Plugin Name: Heartbeat Slowdown [Multisite module]
 * Plugin URI: https://hostmijnpagina.nl/
 * Description: Lower the heartbeat frequency to reduce http requests
 * Author: Sybre Waaijer
 * Author URI: https://cyberwire.nl/
*/

function hmpl_slow_heartbeat( $settings ) {
    $settings['interval'] = 60;
    return $settings;
}
add_filter( 'heartbeat_settings', 'hmpl_slow_heartbeat' );