AFAIK, no case law about the AGPL exists, and opinions differs as to what actions results in the creation of a derivative work. Until case law exists, we cannot know for sure.
OSI's Lawrence Rosen (along with colleague Michael B. Einschlag) seem to say that the only thing that will result in a derivative, is modification of core files.
If their interpretation of the law is correct, then nothing except modification of the core files will create a derivative work.
However, there exists case law (but not about open source) law that indicates that courts may rule on this on other criteria than those listed by Rosen and Einschlag.
So, for the record: I believe Rosen and Einschlag are wrong.
However, I don't think anyone will dispute that if whatever modifications you do is below the threshold of originality (i.e. they are trivial and not copyrightable), then the results of doing this is not a derivative work, as "copyrightability" of the modifications is a legal prerequisite for something being a derivative work.
Let's go through your examples:
But what about using "intended" ways of configuring the CMS? For example, editing its configuration file (e.g., to provide the database login data) or changing settings in the backend (e.g., enabling some checkboxes).
No. This cannot be a derivative, as making such changes to the configuration file are clearly below the threshold of originality.
What about using the built-in plugin manager? For example, installing a new plugin (the plugin manager comes with a plugin browser, which automatically downloads and installs selected plugins), or uninstalling a pre-installed plugin.
If it is somebody else's plugin, freely available for download, then I would again say that what you've done (just downloading and installing it) is below the threshold of originality (i.e. not a derivative).
What about creating a plugin and adding it manually to the plugins folder (and then installing it with the built-in plugin manager)? While the plugin itself might be a derivative work whose source code has to be published in accordance with the AGPL 3.0, does installing this plugin modify the CMS?
If it is a custom plugin that is not otherwise available (i.e. written by you, or somebody you've hired to do this), then creating the plugin itself is above the threshold of originality and therefore a derivative work.
As to whether installing such a plugin would modify the CMS: Yes it would according the FSF's legal team's interpretation of the law about derivative works, but as noted initially, OSI's Larry Rosen seems to disagree.
The licensing FAQ for the Drupal CMS says this about plugins (known as "modules" or "themes", depending on what they do):
Yes. Drupal modules and themes are a derivative work of Drupal. If you distribute them, you must do so under the terms of the GPL version 2 or later.
The Drupal licensing FAQ is written by real lawyers
And again: I believe the FSF and Drupal's lawyers has got this right, and that Rosen and Einschlag are wrong.
What about deleting files the CMS ships with? For example, removing the guide
Again, this is below the threshold of originality, so the removal of this file does not create a derivative work.