Should the type of Boolean categorical features be numerical or categorical after encoding?

There are categorical features which have two different value in my dataframe next to numerical features. I've converted these categorical values to 0 or 1.

I will apply correalation elimination on features after calculating correlation coefficients. Depending on type of features, methods are given below:

Numeric - Numeric: Pearson

Numeric - Categoric: Cramer_V

Categoric - Categoric: Correlation Ratio

That's why I could not be sure what should be type of converted categorical features? Numerical or categorical ?

Another reason to I asked this question is that when I create dummy features for the categorical features which have only two different values, it creates features contains 0 and 1 like how I did manually. So after this process it's taking these features as numerical. But still each value from the feature represents a class and I think feature type should not be numerical.