atoomic

Thanks for your reply, I tested on a fresh installation of WordPress and the API call is working fine.

POST /wp-json/wp-super-cache/v1/settings 
{ "easy": true } # or { "easy": false }

What I can notice is the first time I run the API to enable the plugin it flips the cache_enabled boolean and add a wp_cache_debug_username

--- a/wp-content/wp-cache-config.php
+++ b/wp-content/wp-cache-config.php
@@ -5,12 +5,13 @@ WP-Cache Config Sample File
 See wp-cache.php for author details.
 */

+$wp_cache_debug_username = 'deadbeefdeadbeefdeadbeefdeadbeef';
 $cache_time_interval = 600;
 if ( ! defined('WPCACHEHOME') )
        define( 'WPCACHEHOME', WP_CONTENT_DIR . "/plugins/wp-super-cache/" );

 $cache_compression = 0; // Super cache compression
-$cache_enabled = false;
+$cache_enabled = true;
 $super_cache_enabled = true;
 $cache_max_time = 1800;
 //$use_flock = true; // Set it true or false if you know what to use

Later when accessing the ‘/wp-admin/options-general.php?page=wpsupercache‘ page from a browser some additional values are added to the configuration file. I’m not sure if the plugin works fine without these variable being set?

$wp_cache_home_path = '/';
$wp_cache_slash_check = 1;
$cache_page_secret = 'deadbeefdeadbeefdeadbeefdeadbeef';

Note/ProTip: in order to get the WebAPI working correctly you need to setup redirection in your .htaccess

+++ b/.htaccess
@@ -0,0 +1,15 @@
+# BEGIN WordPress
+# The directives (lines) between "BEGIN WordPress" and "END WordPress" are
+# dynamically generated, and should only be modified via WordPress filters.
+# Any changes to the directives between these markers will be overwritten.
+<IfModule mod_rewrite.c>
+RewriteEngine On
+RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
+RewriteBase /
+RewriteRule ^index\.php$ - [L]
+RewriteCond %{REQUEST_FILENAME} !-f
+RewriteCond %{REQUEST_FILENAME} !-d
+RewriteRule . /index.php [L]
+</IfModule>
+
+# END WordPress#

Thanks with or without these answers, we can close this case.