Reorder coroutine marker check after method unwrapping

Author: Joshua-Ward1

Lib/inspect.py

@@ -307,15 +307,15 @@ def isgeneratorfunction(obj):
 
 def _has_coroutine_mark(f):
     while True:
-        # Direct marker check
-        if getattr(f, "_is_coroutine_marker", None) is _is_coroutine_mark:
-            return True
-
         # Methods: unwrap first (methods cannot be coroutine-marked)
         if ismethod(f):
             f = f.__func__
             continue
 
+        # Direct marker check
+        if getattr(f, "_is_coroutine_marker", None) is _is_coroutine_mark:
+            return True
+
         # Functions created by partialmethod descriptors keep a __partialmethod__ reference
         pm = getattr(f, "__partialmethod__", None)
         if isinstance(pm, functools.partialmethod):
@@ -329,7 +329,6 @@ def _has_coroutine_mark(f):
 
         return False
 
-
 def markcoroutinefunction(func):
     """
     Decorator to ensure callable is recognised as a coroutine function.