Solved.
I had a single newline of white space before <?php in my wp-config.php file which explains why all sites on this multisite were affected. That file like others in the wp-admin folder are shared by every site on the network. This explains why swapping out themes and disabling every plugin didn’t fix the problem.
Mika, your solution to delete wp-admin would have also worked had I seen your reply sooner. It would have given me a fresh wp-config.php file to work with.
Process
I narrowed the whole thing down by installing a fresh multisite on a temporary server. When I uploaded my backups and everything worked I figured the problem had to be in how I set up wp-config.php. As soon as I opened the file and saw the newline of white space in my text editor corrected it and everything magically worked.
It never occurred to me the error was in wp-config and had lived there for a very long time, possibly from the first day I set up the site.
Error Example
? <?php
/**
* The base configurations of the WordPress.
*
* This file has the following configurations: MySQL settings, Table Prefix,
* Secret Keys, WordPress Language, and ABSPATH. You can find more information
* by visiting {@link https://codex.www.ads-software.com/Editing_wp-config.php Editing
* wp-config.php} Codex page. You can get the MySQL settings from your web host.
*
* This file is used by the wp-config.php creation script during the
* installation. You don't have to use the web site, you can just copy this file
* to "wp-config.php" and fill in the values.
*
* @package WordPress
*/
Fixed exmaple
<?php
/**
* The base configurations of the WordPress.
*
* This file has the following configurations: MySQL settings, Table Prefix,
* Secret Keys, WordPress Language, and ABSPATH. You can find more information
* by visiting {@link https://codex.www.ads-software.com/Editing_wp-config.php Editing
* wp-config.php} Codex page. You can get the MySQL settings from your web host.
*
* This file is used by the wp-config.php creation script during the
* installation. You don't have to use the web site, you can just copy this file
* to "wp-config.php" and fill in the values.
*
* @package WordPress
*/
Thanks again Mika, that would be twice I owe you now.