[MilaM]

Here is how I solved the same problem a couple of weeks ago. If you still have an active session in a browser, you can add a recovery e-mail address to you account security settings. After that I was able to add a Yubikey as a second factor without adding a phone number. This should also work if you want to use TOTP as a 2F instead of a Yubikey.

[vort3]

I might try this, thanks.

Yes, I do have session in my browser and I would use it as a second factor to manually approve every login to my account from my browser if I had option to do that, but Google doesn't allow that. You can only confirm logins from android or apple device.

[MilaM]

It worked for me and I did not have to give Google my phone number to "unlock" the other 2FA options and subsequently app passwords. I used the Yubikey, but I think it should work if you only use TOTP.

[vort3]

I added reserve email and in 2FA setup dialog there's still no authenticator option, just Yubikey, notification on Adnroid, or SMS by phone number.