Fix Password Reset Functionality (Bespoke PHP Website)

I have an established bespoke PHP website (not WordPress or a PHP framework) with a password reset function that is no longer working correctly.

I have already investigated the issue and traced the password reset process to `components/forgotten/index.php`. The code appears to reference a legacy SendGrid email implementation that was removed from the site several years ago, while the website's other emails are sent successfully using a different, current email method.

The work required is to:

* Review and confirm the cause of the issue.
* Update the password reset process to use the website's current email sending method.
* Ensure the user only receives a success message if the reset email has actually been sent successfully.
* Test the complete password reset journey from requesting a reset through to successfully changing the password.

This is a small, well-defined project. If we're a good fit, there is likely to be further phased work on the same website.

Please include with your proposal:

* Your experience working with bespoke or legacy PHP applications.
* Similar password reset, authentication or email integration work you have completed.
* Your estimated number of hours to complete this task, with a brief explanation of your estimate.
* Confirmation that you are happy to work initially from the relevant PHP files supplied, rather than requiring full website or hosting access.

If anything is unclear, I would prefer you to ask questions before making changes. I have owned and managed this website for many years and can explain its intended behaviour where required.