Make TaskStatus.started() never return success upon failure

Specifically, make started() reparent the task even if the start() call
is in an effectively cancelled scope when started() is called, and check
sys.exc_info() to prevent calling task_status.started() while handling
active Cancelled(s).

newsfragments/2895.bugfix.rst

@@ -0,0 +1,13 @@
+When :func:`trio.TaskStatus.started` is called in a cancelled scope, it no
+longer returns (indicating that the task has been moved and is now running as a
+child of the nursery) without actually moving the task. Previously,
+:func:`trio.TaskStatus.started` would not move the task in this scenario,
+causing the call to :func:`trio.Nursery.start` to incorrectly wait until the
+started task finished, which caused deadlocks and other issues.
+
+:func:`trio.TaskStatus.started` is no longer allowed to be called by an
+exception handler that is handling one or more :exc:`Cancelled` exceptions;
+attempting to do so will now raise a :exc:`RuntimeError`. Note that any code
+that did this prior to this ban was already buggy, because it was attempting to
+teleport :exc:`Cancelled` exception(s) to a place in the task tree without the
+corresponding :class:`CancelScope`(s) to catch them.

src/trio/_core/_run.py

@@ -856,20 +856,35 @@ def started(self: _TaskStatus[StatusT], value: StatusT) -> None:
     def started(self, value: StatusT | None = None) -> None:
         if self._value is not _NoStatus:
             raise RuntimeError("called 'started' twice on the same task status")
-        self._value = cast(StatusT, value)  # If None, StatusT == None
 
-        # If the old nursery is cancelled, then quietly quit now; the child
-        # will eventually exit on its own, and we don't want to risk moving
-        # children that might have propagating Cancelled exceptions into
-        # a place with no cancelled cancel scopes to catch them.
-        assert self._old_nursery._cancel_status is not None
-        if self._old_nursery._cancel_status.effectively_cancelled:
-            return
+        # Make sure we don't move a task with propagating Cancelled exception(s)
+        # to a place in the tree without the corresponding cancel scope(s).
+        #
+        # N.B.: This check is limited to the task that calls started(). If the
+        # user uses lowlevel.current_task().parent_nursery to add other tasks to
+        # the private implementation-detail nursery of start(), this won't be
+        # able to check those tasks. See #1599.
+        _, exc, _ = sys.exc_info()
+        while exc is not None:
+            handling_cancelled = False
+            if isinstance(exc, Cancelled):
+                handling_cancelled = True
+            elif isinstance(exc, BaseExceptionGroup):
+                matched, _ = exc.split(Cancelled)
+                if matched:
+                    handling_cancelled = True
+            if handling_cancelled:
+                raise RuntimeError(
+                    "task_status.started() cannot be called while handling Cancelled(s)"
+                )
+            exc = exc.__context__
 
         # Can't be closed, b/c we checked in start() and then _pending_starts
         # should keep it open.
         assert not self._new_nursery._closed
 
+        self._value = cast(StatusT, value)  # If None, StatusT == None
+
         # Move tasks from the old nursery to the new
         tasks = self._old_nursery._children
         self._old_nursery._children = set()
@@ -1209,6 +1224,12 @@ async def async_fn(arg1, arg2, *, task_status=trio.TASK_STATUS_IGNORED):
 
         If the child task passes a value to :meth:`task_status.started(value) <TaskStatus.started>`,
         then :meth:`start` returns this value. Otherwise, it returns ``None``.
+
+        :meth:`task_status.started() <TaskStatus.started>` cannot be called by
+        an exception handler (or other cleanup code, like ``finally`` blocks,
+        ``__aexit__`` handlers, and so on) that is handling one or more
+        :exc:`Cancelled` exceptions. (It'll raise a :exc:`RuntimeError` if you
+        violate this rule.)
         """
         if self._closed:
             raise RuntimeError("Nursery is closed to new arrivals")