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.

Alex Moss

Peadig

Disables the default notification email sent by WordPress for an automatic core update. Simply activate the plugin to disable the notification email 🙂
<ul>
<li><a href="http://peadig.com/wordpress-plugins/disable-wordpress-core-update-email/" rel="nofollow ugc">Disable WordPress Core Update Email</a> Plugin homepage.</li>
<li>More <a href="http://peadig.com/wordpress-plugins/" rel="nofollow ugc">WordPress Plugins</a>.</li>
<li>Peadig: A <a href="http://peadig.com/" rel="nofollow ugc">WordPress Bootstrap</a> theme framework.</li>
</ul>

Disable WordPress Core Update Email

The simplicity of the plugin helps it be lightweight & easy to use.

That also means the one line of active PHP code that it consists of (it then being what WordPress recommends in its current documentation per https://wordpress.org/support/article/configuring-automatic-background-updates/#disable-emails-via-filter) is likely to continue to work exactly as expected unless WordPress were to completely overhaul its setup regarding this (with there appearing to be no plans for this.) Especially considering it's using a filter so it's even more flexible if things were to change in the future (won't outright break things due to a code error beyond WordPress doing a fundamental change to a core function like add_filter or __return_false & that'd then break the majority of plugins & themes out there [they'd need a good reason for doing so & it appears they obviously have no plans for doing that either.])

Does exactly what it says it does (even 5 years since last update)

Disables the default notification email sent by WordPress for an automatic core update. Simply activate the plugin to disable the notification email : …

XML-RPC Update Check vs Disable WordPress Core Update Email