Sklearn: Extract feature names after model fitting with polynomialFeature, onehot encoding and OrdinalEncoder

Question

As suggested in many other posts e.g.,

there are ways of extracting relevant feature names. However, How do I make sure that feature names align/are in the same order as the model.coef_?

The structure I have is like:

num1_pre = Pipeline([ ... ])
num2_pre = Pipeline([ ... ])

cat1_pre = Pipeline([("cat_encode", OneHotEncoder())])
cat2_pre = Pipeline([("cat_encode", OrdinalEncoder()) ])

preprocessor = ColumnTransformer([
    ("num1_pre", num1_pre, num_col1), 
    ("num2_pre", num2_pre, num_col2), 
    ("cat1_pre", cat1_pre, cat_col1), 
    ("cat2_pre", cat2_pre, cat_col2)
])

pipeline = Pipeline(steps=[
    ("preprocessor", preprocessor),
    ("poly_features", PolynomialFeatures(interaction_only=True, include_bias=False)),
    ("scaler", StandardScaler()),
    ("model", LinearRegression())
])

My first attempt is to make use of the get_feature_names_out(). I have used CV do obtain a good model:

model = grid_search.best_estimator_
model[:-2].get_feature_names_out()

returns input_features is not equal to feature_names_in_