Try case-insensitive README comparison.

.tools/readmes/render.py

@@ -319,9 +319,12 @@ def write(self):
         print(f"Updated {self.readme_filename}.")
 
     def check(self):
-        try:
-            with open(self.readme_filename, "r", encoding="utf-8") as f:
-                readme_current = f.read()
-                return readme_current == self.readme_text
-        except FileNotFoundError as e:
-            return False
+        actual_filename = self.readme_filename
+        readme_folder, readme_file = os.path.split(self.readme_filename)
+        readme_lower = readme_file.lower()
+        for fname in os.listdir():
+            if fname.lower() == readme_lower:
+                actual_filename = f"{readme_folder}/{fname}"
+        with open(actual_filename, "r", encoding="utf-8") as f:
+            readme_current = f.read()
+            return readme_current == self.readme_text