trogau

You can query core, plugin, and themes individually, or check all at once.
It defines four new methods:
<ul>
<li>xmlrpcCoreUpdateCheck – checks core, returns true/false</li>
<li>xmlrpcPluginUpdateCheck – checks plugins, returns true/false</li>
<li>xmlrpcThemeUpdateCheck – checks themes, returns true/false</li>
<li>xmlrpcUpdatesCheck – checks all of the above, returns an array of trues/falses.</li>
</ul>
The plugin was created primarily for WPUpCheck (http://trog.qgl.org/wpupcheck/), a simple 
Windows application that remotely polls a WordPress site to see if updates are available.

XML-RPC Update Check

This plugin provides XML-RPC methods for checking the update status of WordPress websites.

simshaun

There’s not much to this plugin. It’s a couple barebones filters that turn off the plugin and theme autoupdate emails.
On WordPress 5.5.0, plugin/theme autoupdate emails are turned off regardless of whether or not they failed.
Since WordPress 5.5.1, emails indicating update failures are allowed through.

Disable Plugin Autoupdate Emails

Getting too many "plugin updated" or "theme updated" emails since WordPress 5.5? This turns them off.

XML-RPC Update Check vs Disable Plugin Autoupdate Emails