chore: refactor logs injection configuration (#12921)

We refactor the logic for the enablement of log injection to avoid some
potential circular imports.

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## Reviewer Checklist
- [ ] Reviewer has checked that all the criteria below are met 
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changes
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Author: P403n1x87

ddtrace/_logger.py

@@ -90,15 +90,3 @@ def _add_file_handler(
         logger.addHandler(ddtrace_file_handler)
         logger.debug("ddtrace logs will be routed to %s", log_path)
     return ddtrace_file_handler
-
-
-def _configure_log_injection():
-    """
-    Ensures that logging is patched before we inject trace information into logs.
-    """
-    from ddtrace import patch
-
-    patch(logging=True)
-    ddtrace_logger = logging.getLogger("ddtrace")
-    for handler in ddtrace_logger.handlers:
-        handler.setFormatter(logging.Formatter(DD_LOG_FORMAT))

ddtrace/bootstrap/sitecustomize.py

@@ -22,15 +22,20 @@
 
 from ddtrace.internal.telemetry import telemetry_writer
 from ddtrace import config  # noqa:F401
-from ddtrace._logger import _configure_log_injection
+from ddtrace._logger import DD_LOG_FORMAT
 from ddtrace.internal.logger import get_logger  # noqa:F401
 from ddtrace.internal.module import ModuleWatchdog  # noqa:F401
 from ddtrace.internal.module import is_module_installed
 from ddtrace.internal.utils.formats import asbool  # noqa:F401
 
 # Debug mode from the tracer will do the same here, so only need to do this otherwise.
 if config._logs_injection:
-    _configure_log_injection()
+    from ddtrace import patch
+
+    patch(logging=True)
+    ddtrace_logger = logging.getLogger("ddtrace")
+    for handler in ddtrace_logger.handlers:
+        handler.setFormatter(logging.Formatter(DD_LOG_FORMAT))
 
 
 log = get_logger(__name__)