As you point out, Szilard took steps to keep his nuclear chain-reaction patent secret from the Germans. He later took steps that led the US government to start preventing the open publication of scientific papers on nuclear reactor design and other related topics. (The Germans noticed when the journals went quiet.)

Right after Hiroshima and Nagasaki, he thought the US government was putting out too much public information on the A-bomb. He even thought the Einstein-Szilard letters should remain secret. His idea at the time was the US government should reveal almost nothing and use the promise to reveal as a bargaining chip in an effort to get an international agreement for the control of nuclear weapons.

Szilard's secrecy about the neutron chain-reaction made it hard for him to get anyone to help him work on making nuclear energy practical between 1934 and 1940. So, it arguably slowed down everyone, not just the Germans.

Source is the Szilard biography "Genius in the Shadows"