The newer solution ("Two-factor authentication") also allows non-Apple phones to receive a code on their "trusted phone number". From the support page linked in

The newer solution ("Two-factor authentication") also allows non-Apple phones to receive a code on their "trusted phone number". From the support page linked in a nearby comment: What if I don’t have access to a trusted device or didn't receive a verification code? If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text or a phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device.