[external_files] Skip remote freshness checks during esphome logs

Avoid per-file HTTP HEAD requests during config validation when running
esphome logs against a previously-cached project. The skip_external_update
flag was already plumbed for git operations, but external_files.download_content
ignored it. Thread it through CORE so audio_file, micro_wake_word,
speaker/media_player, image, font, and bme68x_bsec2 reuse cached files
without per-URL network round-trips when the file already exists locally.

tests/unit_tests/test_external_files.py

@@ -236,3 +236,51 @@ def test_download_content_with_network_error_no_cache_fails(
 
     with pytest.raises(Invalid, match="Could not download from.*Network error"):
         external_files.download_content(url, test_file)
+
+
+@patch("esphome.external_files.requests.get")
+@patch("esphome.external_files.has_remote_file_changed")
+def test_download_content_skip_external_update_uses_cache(
+    mock_has_changed: MagicMock, mock_get: MagicMock, setup_core: Path
+) -> None:
+    """Test download_content skips network checks when CORE.skip_external_update is set."""
+    test_file = setup_core / "cached.txt"
+    cached_content = b"cached content"
+    test_file.write_bytes(cached_content)
+
+    CORE.skip_external_update = True
+    try:
+        url = "https://example.com/file.txt"
+        result = external_files.download_content(url, test_file)
+    finally:
+        CORE.skip_external_update = False
+
+    assert result == cached_content
+    mock_has_changed.assert_not_called()
+    mock_get.assert_not_called()
+
+
+@patch("esphome.external_files.requests.get")
+@patch("esphome.external_files.has_remote_file_changed")
+def test_download_content_skip_external_update_downloads_when_missing(
+    mock_has_changed: MagicMock, mock_get: MagicMock, setup_core: Path
+) -> None:
+    """Test download_content still downloads when file is missing, even with skip_external_update."""
+    test_file = setup_core / "missing.txt"
+    new_content = b"fresh content"
+
+    mock_has_changed.return_value = True
+    mock_response = MagicMock()
+    mock_response.content = new_content
+    mock_response.raise_for_status = MagicMock()
+    mock_get.return_value = mock_response
+
+    CORE.skip_external_update = True
+    try:
+        url = "https://example.com/file.txt"
+        result = external_files.download_content(url, test_file)
+    finally:
+        CORE.skip_external_update = False
+
+    assert result == new_content
+    assert test_file.read_bytes() == new_content