It says always I'm not in "sudoers" file!

I migrated from Ubuntu-20 to Debian-12, and I can't excute the command sudo with my username my_name within a fresh installed system. So, I added my_name into "sudo" group(usermod -aG sudo my_name) within a root logged-in terminal, and then rebooted my computer. But it doesn't work, I still get the message like "my_name is not in sudoers file...". I found a strange thing, i.e. when I issue groups command within a terminal window that logged-in as my_name, the "sudo" group name do **NOT** exist in the group list. But when I execute groups my_name with root's permission, the "sudo" group name **DO EXIST** in the group list! Is this a bug of Debian-12? Or I missed some action?