I cannot access Facebook because I do not have an authentication app

I mistakenly logged out from Facebook, so I tried to access again. I didn't remember my password, so I had to reset it with my email. All is fine.

Except now Facebook, as a safety measure, asks to confirm my identity through my authentication app. Which I don't have. I don't even remember if I ever used it year ago, it's not on my current phone as for now.

There are no other options.

Silly enough, I then managed to find my previous password elsewhere, but I cannot use it anymore because I changed it. So Facebook trusts me enough to definitely change a password, but not enough to skip the authentication factor, which I would have expected to confirm the password change.

Any idea on what to do? Thanks!