Installed Steam on a new computer. Signed in. It sent a passcode to my GMail. I signed into GMail. It wanted me to 2FA because I hadn't signed into Google on that device. It sent a notification to my phone, which I never received. I had it resend the notification twice, still nothing. Tried again with my phone's offline passcodes. Neither worked. Tried the QR code/Bluetooth connection, and that finally did it.
At least I got through in the end, but fuck, it's annoying.
Your phone is also likely the least secure device you have. Mine at least has a measly 6 digit password. A human shadowing you could easy watch you input a password and steal your phone.