Override rich.console pipe handler for rich 13.8.0+

Explicitly override `rich.console.Console.on_broken_pipe()` to reraise
the original exception, to bring the behavior of rich 13.8.0+ in line
with older versions.  The new versions instead close output fds and exit
with error instead, which prevents pip's pipe handler from firing.
This is the minimal change needed to make pip's test suite pass after
upgrading vendored rich.

Bug #13006
Bug #13072

src/pip/_internal/utils/logging.py

@@ -137,12 +137,19 @@ def __rich_console__(
             yield Segment("\n")
 
 
+class PipConsole(Console):
+    def on_broken_pipe(self) -> None:
+        # Reraise the original exception, rich 13.8.0+ exits by default
+        # instead, preventing our handler from firing.
+        raise
+
+
 class RichPipStreamHandler(RichHandler):
     KEYWORDS: ClassVar[Optional[List[str]]] = []
 
     def __init__(self, stream: Optional[TextIO], no_color: bool) -> None:
         super().__init__(
-            console=Console(file=stream, no_color=no_color, soft_wrap=True),
+            console=PipConsole(file=stream, no_color=no_color, soft_wrap=True),
             show_time=False,
             show_level=False,
             show_path=False,