Using `add_node` and `dirhtml` causes nodes from `sphinx.ext` to become unknown

Describe the bug

I make an extension that adds a node via add_nodes and use the dirhtml builder. At the same time I include the graphviz extension. This causes the node graphviz to become unknown and Sphinx raises an NotImplementedError:

Traceback
=========

      File "/home/kondziu/.local/share/pipx/venvs/sphinx/lib/python3.12/site-packages/docutils/nodes.py", line 2769, in unknown_departure
        raise NotImplementedError(
    NotImplementedError: <class 'sphinx.writers.html5.HTML5Translator'> departing unknown node type: graphviz

How to Reproduce

conf.py:

import sys, os

sys.path.append(os.path.abspath("."))

extensions = [
    "sphinx.ext.graphviz",
    "extension"
]

extension.py:

import sphinx
import docutils

def ignore(translator, node):
    pass

class TestNode(docutils.nodes.General, docutils.nodes.Element):
    pass

def setup(app: sphinx.application.Sphinx):
    app.add_node(
            node=TestNode, override=False, dirhtml=(ignore, ignore), html=(ignore, ignore)
    )

index.rst:

Test
----

.. graphviz::

  digraph foo {
    rankdir="LR";
    a, b [shape=diamond];
    t1 [label=< <I>true</I> >; shape=box; color=green];
    f1, f2 [label=< <I>false</I> >; shape=box; color=red];
    a -> b [label=1; color=green];
    a -> f1 [label=0; color=red];
    b -> t1 [label=1; color=green];
    b -> f2 [label=0; color=red];
  }

Build with:

sphinx-build -b html . _build/            # works fine
sphinx-build -b dirhtml . _build/       # fails

Zip: example.zip

Environment Information

Sphinx 9.1.0

Sphinx extensions

extensions = [
    "sphinx.ext.graphviz",
    "extension"  # custom extension, see description
]

Additional context

Workaround:

    # The graphviz node is not defined for `dirhtml`.
    app.add_node(
        node=sphinx.ext.graphviz.graphviz,
        override=True,
        html=(sphinx.ext.graphviz.html_visit_graphviz, None),
        dirhtml=(sphinx.ext.graphviz.html_visit_graphviz, None),
        latex=(sphinx.ext.graphviz.latex_visit_graphviz, None),
        texinfo=(sphinx.ext.graphviz.texinfo_visit_graphviz, None),
        text=(sphinx.ext.graphviz.text_visit_graphviz, None),
        man=(sphinx.ext.graphviz.man_visit_graphviz, None),
    )

Start with the minimal conf.py, extension.py, and index.rst reproducer, then run the html and dirhtml sphinx-build commands. Inspect how sphinx.ext.graphviz registers its node for each builder alongside the custom add_node call. Done means the dirhtml build no longer treats graphviz as an unknown node while the html build continues to work.