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.
I fucking hate Steam’s 2FA. Forcing you to use their app instead of your preferred authentication service. Years ago I got pretty thoroughly locked out because I switched phones and was logged out of my Steam account on my PC. Can’t remember how I resolved it, but I think it took contacting their support team.
Similar happened to me. Got locked out of steam for ages.