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.
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Generally, gender can not  be considered  - true or false . Classification is based on sex - Male or female  . Categories differ and can be assigned particular  numerical values (dummy variable) 1, 2 or 2, 3 etc. Binary variable is different. If you want to find correlation  between  the scores obtained by Male students and female students,  you will have to have matched pairs. Categories measure the levels for grouping. Binary classification can be undertaken for a dependent  variable in regression analysis or point biserial correlation. The standard softwares for statistical analysis do not invoke 0,1 as variable. The probability based solutions may use this classification for grouping.