Clustering with categorical as well as numerical features
thank you for your question, which asks about how to represent categorical variables in clustering.
The main way that we represent any categorical variable is to represent them as one-hot encodings (https://machinelearningmastery.com/why-one-hot-encode-data-in-machine-learning/).
After converting our categorical variables to one-hot encodings, we simply concatenate these vectors with our numerical values (which should be normalised!) to make a long / high-dimensional vector for a particular example in your dataset.