diff --git a/mypy/stubutil.py b/mypy/stubutil.py
--- a/mypy/stubutil.py
+++ b/mypy/stubutil.py
@@ -614,10 +614,24 @@ def get_imports(self) -> str:
 
     def output(self) -> str:
         """Return the text for the stub."""
-        imports = self.get_imports()
-        if imports and self._output:
-            imports += "\n"
-        return imports + "".join(self._output)
+        pieces: list[str] = []
+        if imports := self.get_imports():
+            pieces.append(imports)
+        if dunder_all := self.get_dunder_all():
+            pieces.append(dunder_all)
+        if self._output:
+            pieces.append("".join(self._output))
+        return "\n".join(pieces)
+
+    def get_dunder_all(self) -> str:
+        """Return the __all__ list for the stub."""
+        if self._all_:
+            # Note we emit all names in the runtime __all__ here, even if they
+            # don't actually exist. If that happens, the runtime has a bug, and
+            # it's not obvious what the correct behavior should be. We choose
+            # to reflect the runtime __all__ as closely as possible.
+            return f"__all__ = {self._all_!r}\n"
+        return ""
 
     def add(self, string: str) -> None:
         """Add text to generated stub."""
@@ -651,8 +665,7 @@ def set_defined_names(self, defined_names: set[str]) -> None:
         self.defined_names = defined_names
         # Names in __all__ are required
         for name in self._all_ or ():
-            if name not in self.IGNORED_DUNDERS:
-                self.import_tracker.reexport(name)
+            self.import_tracker.reexport(name)
 
         # These are "soft" imports for objects which might appear in annotations but not have
         # a corresponding import statement.
@@ -751,7 +764,13 @@ def is_private_name(self, name: str, fullname: str | None = None) -> bool:
             return False
         if name == "_":
             return False
-        return name.startswith("_") and (not name.endswith("__") or name in self.IGNORED_DUNDERS)
+        if not name.startswith("_"):
+            return False
+        if self._all_ and name in self._all_:
+            return False
+        if name.startswith("__") and name.endswith("__"):
+            return name in self.IGNORED_DUNDERS
+        return True
 
     def should_reexport(self, name: str, full_module: str, name_is_alias: bool) -> bool:
         if (
@@ -761,18 +780,21 @@ def should_reexport(self, name: str, full_module: str, name_is_alias: bool) -> b
         ):
             # Special case certain names that should be exported, against our general rules.
             return True
+        if name_is_alias:
+            return False
+        if self.export_less:
+            return False
+        if not self.module_name:
+            return False
         is_private = self.is_private_name(name, full_module + "." + name)
+        if is_private:
+            return False
         top_level = full_module.split(".")[0]
         self_top_level = self.module_name.split(".", 1)[0]
-        if (
-            not name_is_alias
-            and not self.export_less
-            and (not self._all_ or name in self.IGNORED_DUNDERS)
-            and self.module_name
-            and not is_private
-            and top_level in (self_top_level, "_" + self_top_level)
-        ):
+        if top_level not in (self_top_level, "_" + self_top_level):
             # Export imports from the same package, since we can't reliably tell whether they
             # are part of the public API.
-            return True
-        return False
+            return False
+        if self._all_:
+            return name in self._all_
+        return True

diff --git a/test-data/unit/stubgen.test b/test-data/unit/stubgen.test
--- a/test-data/unit/stubgen.test
+++ b/test-data/unit/stubgen.test
@@ -587,6 +587,8 @@ __all__ = [] + ['f']
 def f(): ...
 def g(): ...
 [out]
+__all__ = ['f']
+
 def f() -> None: ...
 
 [case testOmitDefsNotInAll_semanal]
@@ -594,6 +596,8 @@ __all__ = ['f']
 def f(): ...
 def g(): ...
 [out]
+__all__ = ['f']
+
 def f() -> None: ...
 
 [case testOmitDefsNotInAll_inspect]
@@ -601,6 +605,8 @@ __all__ = [] + ['f']
 def f(): ...
 def g(): ...
 [out]
+__all__ = ['f']
+
 def f(): ...
 
 [case testVarDefsNotInAll_import]
@@ -610,6 +616,8 @@ x = 1
 y = 1
 def g(): ...
 [out]
+__all__ = ['f', 'g']
+
 def f() -> None: ...
 def g() -> None: ...
 
@@ -620,6 +628,8 @@ x = 1
 y = 1
 def g(): ...
 [out]
+__all__ = ['f', 'g']
+
 def f(): ...
 def g(): ...
 
@@ -628,6 +638,8 @@ __all__ = [] + ['f']
 def f(): ...
 class A: ...
 [out]
+__all__ = ['f']
+
 def f() -> None: ...
 
 class A: ...
@@ -637,6 +649,8 @@ __all__ = [] + ['f']
 def f(): ...
 class A: ...
 [out]
+__all__ = ['f']
+
 def f(): ...
 
 class A: ...
@@ -647,6 +661,8 @@ class A:
     x = 1
     def f(self): ...
 [out]
+__all__ = ['A']
+
 class A:
     x: int
     def f(self) -> None: ...
@@ -684,6 +700,8 @@ x = 1
 [out]
 from re import match as match, sub as sub
 
+__all__ = ['match', 'sub', 'x']
+
 x: int
 
 [case testExportModule_import]
@@ -694,6 +712,8 @@ y = 2
 [out]
 import re as re
 
+__all__ = ['re', 'x']
+
 x: int
 
 [case testExportModule2_import]
@@ -704,6 +724,8 @@ y = 2
 [out]
 import re as re
 
+__all__ = ['re', 'x']
+
 x: int
 
 [case testExportModuleAs_import]
@@ -714,6 +736,8 @@ y = 2
 [out]
 import re as rex
 
+__all__ = ['rex', 'x']
+
 x: int
 
 [case testExportModuleInPackage_import]
@@ -722,6 +746,8 @@ __all__ = ['p']
 [out]
 import urllib.parse as p
 
+__all__ = ['p']
+
 [case testExportPackageOfAModule_import]
 import urllib.parse
 __all__ = ['urllib']
@@ -729,6 +755,8 @@ __all__ = ['urllib']
 [out]
 import urllib as urllib
 
+__all__ = ['urllib']
+
 [case testRelativeImportAll]
 from .x import *
 [out]
@@ -741,6 +769,8 @@ x = 1
 class C:
     def g(self): ...
 [out]
+__all__ = ['f', 'x', 'C', 'g']
+
 def f() -> None: ...
 
 x: int
@@ -758,6 +788,8 @@ x = 1
 class C:
     def g(self): ...
 [out]
+__all__ = ['f', 'x', 'C', 'g']
+
 def f(): ...
 
 x: int
@@ -2343,6 +2375,8 @@ else:
 [out]
 import cookielib as cookielib
 
+__all__ = ['cookielib']
+
 [case testCannotCalculateMRO_semanal]
 class X: pass
 
@@ -2788,6 +2822,8 @@ class A: pass
 # p/__init__.pyi
 from p.a import A
 
+__all__ = ['a']
+
 a: A
 # p/a.pyi
 class A: ...
@@ -2961,7 +2997,9 @@ __uri__ = ''
 __version__ = ''
 
 [out]
-from m import __version__ as __version__
+from m import __about__ as __about__, __author__ as __author__, __version__ as __version__
+
+__all__ = ['__about__', '__author__', '__version__']
 
 [case testAttrsClass_semanal]
 import attrs

Maybe __all__ should be added explicitly in stubgen
**Feature**

(A clear and concise description of your feature proposal.)

Maybe `__all__` should be added explicitly in stubgen.

**Pitch**

(Please explain why this feature should be implemented and how it would be used. Add examples, if applicable.)

Adding `__all__` to type stubs explicitly can avoid some error. For example:

├── test
│   └── __init__.py


\_\_init\_\_.py:
```python
class Test:
    pass

__all__ = []
```

The type stub file generated by stubgen is
\_\_init\_\_.pyi:
```python
class Test: ...
```

When using `from .test import *` to import test as a submodule, `Test` will be imported according to the type stub, while in fact `Test` should not be used.

**A Possible Implement**

Replace `output(self)` in stubgen.py by following implement:
```python
    def output(self) -> str:
        """Return the text for the stub."""
        imports = ''
        if self._import_lines:
            imports += ''.join(self._import_lines)
        imports += ''.join(self.import_tracker.import_lines())
        if imports and self._output:
            imports += '\n'
        imports += ''.join(self._output)
        """export __all__ when it's defined"""
        if imports and self._all_ != None:
            imports += '\n'
        if self._all_ != None:
            imports += '__all__ = ['
            for name in self._all_:
                imports += ''.join(('\"', name, '\", '))
            imports += ']'
        return imports
```

mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testExportPackageOfAModule_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testVarDefsNotInAll_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testExportModule2_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testExportModuleInPackage_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testOmitDefsNotInAll_semanal mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testExportModule_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testExportModuleAs_import mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testOmitDefsNotInAll_inspect
mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testRelativeImportAll mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testCannotCalculateMRO_semanal mypy/test/teststubgen.py::StubgenPythonSuite::stubgen.test::testAttrsClass_semanal