I don't think there is any one "best" way to analyze interview questions, but the most common way is undoubtedly through Thematic Analysis, as described by Braun and Clarke. Their 2006 article on TA has received over 150,000 citations, but for the most current version, I would recommend their 2023 book Thematic Analysis: A Practical Guide from Sage.
I agree with the two mentioned methods. In my experience these two approaches are very much linked to geographic/language issues. Thematic analysis is in my experience more commonly used in the English speaking world, whereas content analysis is very dominant in German speaking countries.
Two prominent German speaking authors are Udo Kuckartz and Philipp Mayring - both of whom have also published some English texts, e.g.: