Hello,
Thank you for your query, and we are so sorry about the trouble this must have caused.
We logged in to your site using the credentials provided in the sensitive data section of the ticket.
Upon checking we could see that you have set the “Fallback Behavior” feature of the Rank Math plugin as “Redirect to Homepage” instead of “Default 404” under WordPress Dashboard > Rank Math > General Settings > Redirections.

We have set it to “Default 404” and went ahead to /plugins/seo-by-rank-math/includes/modules/404-monitor/class-monitor.php
in line 46, and replaced it using the WP File Manager Plugin:
From this :
$this->action( $this->get_hook(), 'capture_404' );
To this one :
$this->action('template_redirect', 'capture_404' );
Now the 404 logs appear as expected.

Please be advised that, the solution will be overwritten, when you’ll update Rank Math in your site next time. Once you update Rank Math, you’ll need to edit the file and replace the line just as mentioned above. However, till the next update, this should work without any issue.
The 404 template redirect could be coming from your theme and since by default, Rank Math can’t read these types of templates, you need to apply the solution presented above.
Unfortunately, we don’t support this type of template at the moment so you may need to rely on this workaround applied to your website for now.
We hope that helps, and please don’t hesitate to get in touch if you have any other questions.
Thank you.