Add pixi example (#12155)

Pixi is a modern package manager for the conda ecosystem. It's much
faster than conda/mamba and also supports lockfiles natively.
You can install pixi via asdf
(https://github.com/asdf-vm/asdf-plugins/blob/master/plugins/pixi) so
the usage within mkdocs should be fairly straightforward.

<!-- readthedocs-preview docs start -->
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:books: Documentation previews :books:

- User's documentation (`docs`):
https://docs--12155.org.readthedocs.build/12155/

<!-- readthedocs-preview docs end -->

<!-- readthedocs-preview dev start -->
- Developer's documentation (`dev`):
https://dev--12155.org.readthedocs.build/12155/

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Co-authored-by: Eric Holscher <[email protected]>

Author: pavelzw

docs/user/build-customization.rst

@@ -512,6 +512,35 @@ This example uses ``pip`` and installs from a group named ``docs``:
 For more information on relevant ``pip`` usage, see the
 `pip user guide on Dependency Groups <https://pip.pypa.io/en/stable/user_guide/#dependency-groups>`_.
 
+Install dependencies with ``pixi``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Projects can use `pixi <https://github.com/prefix-dev/pixi/>`__,
+to install Python dependencies, usually reducing the time taken to install compared to conda or pip.
+Take a look at the following example:
+
+
+.. code-block:: yaml
+   :caption: .readthedocs.yaml
+
+   version: 2
+
+   build:
+      os: ubuntu-24.04
+      jobs:
+         create_environment:
+            - asdf plugin add pixi
+            - asdf install pixi latest
+            - asdf global pixi latest
+         install:
+            # assuming you have an environment called "docs"
+            - pixi install -e docs
+         build:
+            html:
+               - pixi run -e docs sphinx-build -T -b html docs $READTHEDOCS_OUTPUT/html
+
+MkDocs projects could use ``NO_COLOR=1 pixi run -e docs mkdocs build --strict --site-dir $READTHEDOCS_OUTPUT/html`` instead.
+
 Update Conda version
 ~~~~~~~~~~~~~~~~~~~~