I am not sure that is always the case anymore. I am quite involved with the League of Women Voters in my state. They helped register new citizens, but are now being prohibited from registering new citizens at naturalization events. Given this, it would surprise me if the government were doing it. I hope that I am wrong.
https://www.npr.org/2025/09/02/nx-s1-5525875/trump-naturalization-voter-registration-uscis