Fix deprecated call to mimetypes.guess_type in CachingStaticResource (h…

…ome-assistant#132299)

homeassistant/components/http/static.py

@@ -4,6 +4,7 @@
 
 from collections.abc import Mapping
 from pathlib import Path
+import sys
 from typing import Final
 
 from aiohttp.hdrs import CACHE_CONTROL, CONTENT_TYPE
@@ -17,6 +18,15 @@
 CACHE_HEADERS: Mapping[str, str] = {CACHE_CONTROL: CACHE_HEADER}
 RESPONSE_CACHE: LRU[tuple[str, Path], tuple[Path, str]] = LRU(512)
 
+if sys.version_info >= (3, 13):
+    # guess_type is soft-deprecated in 3.13
+    # for paths and should only be used for
+    # URLs. guess_file_type should be used
+    # for paths instead.
+    _GUESSER = CONTENT_TYPES.guess_file_type
+else:
+    _GUESSER = CONTENT_TYPES.guess_type
+
 
 class CachingStaticResource(StaticResource):
     """Static Resource handler that will add cache headers."""
@@ -37,9 +47,7 @@ async def _handle(self, request: Request) -> StreamResponse:
                 # Must be directory index; ignore caching
                 return response
             file_path = response._path  # noqa: SLF001
-            response.content_type = (
-                CONTENT_TYPES.guess_type(file_path)[0] or FALLBACK_CONTENT_TYPE
-            )
+            response.content_type = _GUESSER(file_path)[0] or FALLBACK_CONTENT_TYPE
             # Cache actual header after setter construction.
             content_type = response.headers[CONTENT_TYPE]
             RESPONSE_CACHE[key] = (file_path, content_type)