[core] Catch body-read errors in download_content

`requests.Response.content` reads the body lazily, so chunked-decode,
gzip-decode, and mid-stream connection drops all surface as
RequestException subclasses on first access -- not from requests.get
itself. The previous code accessed `.content` outside the surrounding
try/except, so any of those (rare but real) errors would propagate
out of download_content instead of falling back to the cached file
or raising the user-friendly cv.Invalid.

Move `data = req.content` inside the try block so the existing error
path handles it. Two new tests cover the with-cache and no-cache
branches using a `ChunkedEncodingError` injected on `.content`.

tests/unit_tests/test_external_files.py

@@ -238,6 +238,59 @@ def test_download_content_with_network_error_no_cache_fails(
         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_with_body_read_error_uses_cache(
+    mock_has_changed: MagicMock, mock_get: MagicMock, setup_core: Path
+) -> None:
+    """Body-read errors (chunked-decode/gzip-decode/mid-stream connection
+    drop) raise RequestException subclasses on `.content` access, not from
+    `requests.get` itself. They must follow the same fall-back-to-cache
+    path as a connect-time failure.
+    """
+    test_file = setup_core / "cached.txt"
+    cached_content = b"cached content"
+    test_file.write_bytes(cached_content)
+
+    mock_has_changed.return_value = True
+    mock_response = MagicMock()
+    mock_response.raise_for_status = MagicMock()
+    type(mock_response).content = property(
+        lambda self: (_ for _ in ()).throw(
+            requests.exceptions.ChunkedEncodingError("body truncated")
+        )
+    )
+    mock_get.return_value = mock_response
+
+    result = external_files.download_content("https://example.com/file.txt", test_file)
+
+    assert result == cached_content
+
+
+@patch("esphome.external_files.requests.get")
+@patch("esphome.external_files.has_remote_file_changed")
+def test_download_content_with_body_read_error_no_cache_fails(
+    mock_has_changed: MagicMock, mock_get: MagicMock, setup_core: Path
+) -> None:
+    """A body-read failure with no cache available must surface as a
+    cv.Invalid, same as a connect-time failure with no cache.
+    """
+    test_file = setup_core / "nonexistent.txt"
+
+    mock_has_changed.return_value = True
+    mock_response = MagicMock()
+    mock_response.raise_for_status = MagicMock()
+    type(mock_response).content = property(
+        lambda self: (_ for _ in ()).throw(
+            requests.exceptions.ChunkedEncodingError("body truncated")
+        )
+    )
+    mock_get.return_value = mock_response
+
+    with pytest.raises(Invalid, match="Could not download from.*body truncated"):
+        external_files.download_content("https://example.com/file.txt", 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(