I learned about as much about turn of the century Vienna, the Vienna Circle, and Nazi-occupied Austria as I did about Gödel's ideas. This was very much a 'life of'. But otherwise, well written enough. Came across another book about Moritz Schlick's murder that I may check out.
Further reading: The Murder of Professor Schlick: The Rise and Fall of the Vienna Circle, Edmonds D., 2020 Incompleteness: The Proof and Paradox of Kurt Gödel, Goldstein R., 2005 Logicomix, Christos Papadimitriou, 2008 (read a long time ago, remember enjoying, and worth finding again)