fix(asm): improve BlockingException catch for fastapi [backport 2.21] (#12424)

Backport f3e0eb3 from #12413 to 2.21.

Fastapi middleware use BaseExceptionGroup on python 3.11. With a custom
middleware, this mechanism could encapsulate BlockingException raised by
our blocking mechanism, preventing it to be properly caught to generate
a proper blocking response.

This will be tested permanently by the `fastapi` weblog, as
DataDog/system-tests#4125 adds a custom
middleware to simulate ATO automatic instrumentation.

Due to our mandatory compatibility with previous python version, we
can't use syntaxic sugar to handle exception group.


## Checklist
- [x] PR author has checked that all the criteria below are met
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- The PR description articulates the motivation for the change
- The change includes tests OR the PR description describes a testing
strategy
- The PR description notes risks associated with the change, if any
- Newly-added code is easy to change
- The change follows the [library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
- The change includes or references documentation updates if necessary
- Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist
- [x] Reviewer has checked that all the criteria below are met 
- Title is accurate
- All changes are related to the pull request's stated goal
- Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes
- Testing strategy adequately addresses listed risks
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- If necessary, author has acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment
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[release branch maintenance
policy](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting)

Co-authored-by: Christophe Papazian <[email protected]>

Author: github-actions[bot]

ddtrace/contrib/internal/asgi/middleware.py

@@ -318,6 +318,14 @@ async def wrapped_blocked_send(message):
                 span.set_exc_info(exc_type, exc_val, exc_tb)
                 self.handle_exception_span(exc, span)
                 raise
+            except BaseException as exception:
+                # managing python 3.11+ BaseExceptionGroup with compatible code for 3.10 and below
+                if exception.__class__.__name__ == "BaseExceptionGroup":
+                    for exc in exception.exceptions:
+                        if isinstance(exc, BlockingException):
+                            set_blocked(exc.args[0])
+                            return await _blocked_asgi_app(scope, receive, wrapped_blocked_send)
+                raise
             finally:
                 if span in scope["datadog"]["request_spans"]:
                     scope["datadog"]["request_spans"].remove(span)

releasenotes/notes/fix_blocking_on_fastapi_with_middleware-08ac58a6b112e29f.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    ASM: This fix resolves an issue where blocking mechanism could partially fail with a 500 error on fastapi with python>=3.11 with a custom middleware.
+