diff --git a/sphinx/domains/_domains_container.py b/sphinx/domains/_domains_container.py
index c109e1a41c9..3166753c321 100644
--- a/sphinx/domains/_domains_container.py
+++ b/sphinx/domains/_domains_container.py
@@ -199,7 +199,7 @@ def __delattr__(self, key: str) -> None:
             raise TypeError(msg)
         super().__delattr__(key)
 
-    # Mapping interface
+    # Mapping interface: builtin domains
 
     @overload
     def __getitem__(self, key: Literal["c"]) -> CDomain:
@@ -241,6 +241,8 @@ def __getitem__(self, key: Literal["rst"]) -> ReSTDomain:
     def __getitem__(self, key: Literal["std"]) -> StandardDomain:
         ...
 
+    # Mapping interface: first-party domains
+
     @overload
     def __getitem__(self, key: Literal["duration"]) -> DurationDomain:
         ...
@@ -249,6 +251,8 @@ def __getitem__(self, key: Literal["duration"]) -> DurationDomain:
     def __getitem__(self, key: Literal["todo"]) -> TodoDomain:
         ...
 
+    # Mapping interface: third-party domains
+
     @overload
     def __getitem__(self, key: str) -> Domain:
         ...
diff --git a/sphinx/ext/autosummary/__init__.py b/sphinx/ext/autosummary/__init__.py
index 5a6a741f78c..01a79563f38 100644
--- a/sphinx/ext/autosummary/__init__.py
+++ b/sphinx/ext/autosummary/__init__.py
@@ -152,7 +152,7 @@ def autosummary_table_visit_html(self: HTML5Translator, node: autosummary_table)
 # -- autodoc integration -------------------------------------------------------
 
 class FakeApplication:
-    def __init__(self, *, registry: SphinxComponentRegistry) -> None:
+    def __init__(self) -> None:
         self.doctreedir = None
         self.events = None
         self.extensions: dict[str, Extension] = {}
@@ -160,14 +160,13 @@ def __init__(self, *, registry: SphinxComponentRegistry) -> None:
         self.config = Config()
         self.project = Project('', {})
         self.registry = SphinxComponentRegistry()
-        # self.registry.domains |= registry.domains
 
 
 class FakeDirective(DocumenterBridge):
-    def __init__(self, *, registry: SphinxComponentRegistry) -> None:
+    def __init__(self) -> None:
         settings = Struct(tab_width=8)
         document = Struct(settings=settings)
-        app = FakeApplication(registry=registry)
+        app = FakeApplication()
         app.config.add('autodoc_class_signature', 'mixed', 'env', ())
         env = BuildEnvironment(app)  # type: ignore[arg-type]
         state = Struct(document=document)
@@ -194,11 +193,10 @@ def get_documenter(app: Sphinx, obj: Any, parent: Any) -> type[Documenter]:
     else:
         parent_doc_cls = ModuleDocumenter
 
-    bridge = FakeDirective(registry=app.registry)
     if hasattr(parent, '__name__'):
-        parent_doc = parent_doc_cls(bridge, parent.__name__)
+        parent_doc = parent_doc_cls(FakeDirective(), parent.__name__)
     else:
-        parent_doc = parent_doc_cls(bridge, "")
+        parent_doc = parent_doc_cls(FakeDirective(), "")
 
     # Get the correct documenter class for *obj*
     classes = [cls for cls in app.registry.documenters.values()
diff --git a/sphinx/testing/util.py b/sphinx/testing/util.py
index 58608dcdc7d..f99442eb004 100644
--- a/sphinx/testing/util.py
+++ b/sphinx/testing/util.py
@@ -123,7 +123,7 @@ def __init__(
         # unknown keyword arguments
         **extras: Any,
     ) -> None:
-        self._buildername = buildername
+        self._builder_name = buildername
 
         assert srcdir is not None
 
@@ -211,7 +211,7 @@ def cleanup(self, doctrees: bool = False) -> None:
             os.remove(self.docutils_conf_path)
 
     def __repr__(self) -> str:
-        return f'<{self.__class__.__name__} buildername={self._buildername!r}>'
+        return f'<{self.__class__.__name__} buildername={self._builder_name!r}>'
 
     def build(self, force_all: bool = False, filenames: list[str] | None = None) -> None:
         self.env._pickled_doctree_cache.clear()
diff --git a/tests/test_search.py b/tests/test_search.py
index dfbda5d4726..a0c4cc0859f 100644
--- a/tests/test_search.py
+++ b/tests/test_search.py
@@ -5,6 +5,7 @@
 import json
 import warnings
 from io import BytesIO
+from typing import TYPE_CHECKING
 
 import pytest
 from docutils import frontend, utils
@@ -14,6 +15,9 @@
 
 from tests.utils import TESTS_ROOT
 
+if TYPE_CHECKING:
+    from collections.abc import Iterator
+
 JAVASCRIPT_TEST_ROOTS = [
     directory
     for directory in (TESTS_ROOT / 'js' / 'roots').iterdir()
@@ -22,30 +26,30 @@
 
 
 class DummyDomainsContainer:
-    def __init__(self, domains):
+    def __init__(self, **domains: DummyDomain) -> None:
         self._domain_instances = domains
 
-    def sorted_domains(self):
+    def sorted_domains(self) -> Iterator[DummyDomain]:
         for _domain_name, domain in sorted(self._domain_instances.items()):
             yield domain
 
 
 class DummyEnvironment:
-    def __init__(self, version, domains):
+    def __init__(self, version: str, domains: DummyDomainsContainer) -> None:
         self.version = version
-        self.domains = DummyDomainsContainer(domains)
+        self.domains = domains
 
-    def __getattr__(self, name):
+    def __getattr__(self, name: str):
         if name.startswith('_search_index_'):
             setattr(self, name, {})
         return getattr(self, name, {})
 
-    def __str__(self):
+    def __str__(self) -> str:
         return f'DummyEnvironment({self.version!r}, {self.domains!r})'
 
 
 class DummyDomain:
-    def __init__(self, name, data):
+    def __init__(self, name: str, data: dict) -> None:
         self.name = name
         self.data = data
         self.object_types = {}
@@ -186,7 +190,7 @@ def test_IndexBuilder():
             ('objname2', 'objdispname2', 'objtype2', 'docname2_2', '', -1),
         ],
     )
-    env = DummyEnvironment('1.0', {'dummy1': domain1, 'dummy2': domain2})
+    env = DummyEnvironment('1.0', DummyDomainsContainer(dummy1=domain1, dummy2=domain2))
     doc = utils.new_document(b'test data', settings)
     doc['file'] = 'dummy'
     parser.parse(FILE_CONTENTS, doc)
@@ -274,7 +278,7 @@ def test_IndexBuilder():
         1: ('dummy2', 'objtype1', 'objtype1'),
     }
 
-    env = DummyEnvironment('1.0', {'dummy1': domain1, 'dummy2': domain2})
+    env = DummyEnvironment('1.0', DummyDomainsContainer(dummy1=domain1, dummy2=domain2))
 
     # dump / load
     stream = BytesIO()