Scott Reilly

This plugin adds a checkbox to the profile page for users which allows them to opt into receiving a notification email whenever a comment is made to the site.
If a comment goes into moderation, only users who have the ability to manage comments on the site will receive the moderation notification email.
By default, all users of the site have the ability to subscribe to notifications about comments. A filter is provided to facilitate use of code to customize the feature’s availability to users.
Note: a “user” is a person with an actual login account for the site. The plugin does not facilitate permitting visitors who do not have an account on the site to be able to subscribe to all comments.
Links: <a href="http://coffee2code.com/wp-plugins/optin-comment-notifications/" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/optin-comment-notifications/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/optin-comment-notifications/" rel="nofollow ugc">GitHub</a> | <a href="http://coffee2code.com" rel="nofollow ugc">Author Homepage</a>

Optin Comment Notifications

Checkboxes on user profiles to receive emails about new comments. Like it says.

Exactly what you want

Allows users to opt into receiving a notification email whenever a comment is made to the site.

This plugin enables a user with the administrator role the ability to comment on any post or page, even if the comments for that post or page are closed. When the plugin is active, this behavior is automatically enabled.
Administrators can be explicitly prevented from commenting on specific posts via two approaches:
<ul>
<li>When creating or editing a post, in the “Prevent Admin Comments” metabox (in the block editor) or the “Discussion” metabox (in the classic editor) there is a checkbox labeled “Prevent administrators from commenting” that only administrators can access. Checking the checkbox will prevent administrators from commenting on the post even though this plugin is active. (If the metabox isn’t visible for you when using the classic editor, then expand the “Screen Options” slide-down panel on the upper-right of the page.)</li>
<li>Programmatically, via the use of the ‘c2c_admin_can_always_comment_disable’ filter. This can be used be provide more fine-grained access control and contextual handling. See the “Hooks” section for documentation on the filter’s use.</li>
</ul>
Links: <a href="https://coffee2code.com/wp-plugins/always-allow-admin-comments/" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/always-allow-admin-comments/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/always-allow-admin-comments/" rel="nofollow ugc">GitHub</a> | <a href="https://coffee2code.com" rel="nofollow ugc">Author Homepage</a>
<h3>Developer Documentation</h3>
Developer documentation can be found in <a href="https://github.com/coffee2code/always-allow-admin-comments/blob/master/DEVELOPER-DOCS.md" rel="nofollow ugc">DEVELOPER-DOCS.md</a>. That documentation covers the hooks provided by the plugin.
As an overview, these are the hooks provided by the plugin:
<ul>
<li><code>c2c_always_allow_admin_comments_disable</code> : Customizes if comments should actually be disabled for a particular admin user.</li>
<li><code>c2c_always_allow_admin_comments_post_types</code>: Customizes which post types are supported by the plugin.</li>
</ul>

Always Allow Admin Comments

Allow an admin user (when logged in) to always be able to comment on a post, even if comments are closed for the post.

Optin Comment Notifications vs Always Allow Admin Comments