@biltongandpotroast I think there is some misunderstanding on your side. When the Pre-Update check warns of the phpmailer libraries not being compatible, that doesn't mean that these libraries are obsolete. It means that they are not compatible with Joomla 4 in the versions which are available on Joomla 3. But they will be updated with the core when updating the CMS to 4. See here the PR which updated it for Joomla 4: #34598 . And if you check the installation package of any Joomla 4.x version you will see the phpmailer is still included.

With the simplepie you are right, it is obsolete in Joomla 4, and so it is removed with the update, see here for the code: https://github.com/joomla/joomla-cms/blob/4.3-dev/administrator/components/com_admin/script.php#L6858-L6872 . So if these folders still are there after the update, then your update has not run completely. This makes me ask: How have you updated? Have you used the Joomla Update component like it should be, and has the update run without any errors? Or have there been errors, or have you used an old, unsupported method for updating like e.g. just uploading and unpacking the zip file and then running the database fixer? That would not work and is unsupported since 3.4 or 3.5.

Closing as there is nothing to do here. The question was answered