Improve favicon support by incorporating `sphinx-favicon` in `sphix.ext`

Is your feature request related to a problem? Please describe.
Lots of things have changed since the last time adding a icon to the documentation was simply achieved by having a favicon.ico file.

The folks from evil martians did a very nice research on the topic and realised that, if we ignore old browsers/versions of browsers, 6 icon files cover most of the cases.

However, with Sphinx we can only specify one (without setting any attribute like the content-type).

Describe the solution you'd like
@tcmetzger did an amazing work by creating sphinx-favicon which can be used in this scenario.

Recently, there was a discussion in the setuptools repository, where it was mentioned that maybe it would be nice to have this extension directly under the sphinx package.

The intention of this issue is to start a discussion with sphinx and sphinx-favicon maintainers see if both sides have interest on making sphinx-favicon part of the sphinx repository (alongside the other sphinx.ext packages).

Describe alternatives you've considered
One alternative is keeping sphinx-favicon as it is currently is, a separated package, which is not bad. But some people consider this use-case so common that it would be nice to have it supported out of the box.

The other alternative is for sphinx to support the use case directly, without the need of extensions.

Start by reviewing the existing sphinx.ext packages and the linked sphinx-favicon project, then read the discussion referenced in the issue. Determine whether maintainers want to adopt the extension or support multiple favicon files directly; done requires an agreed scope and implementation plan, since no target files or tests are identified.