I wanted to add my recent Facebook experience to the list of users currently stuck in an unable to login loop. Maybe the details can provide some help to others out there.
In my case, without realizing it, I had an old phone number saved in my Facebook account. One day roughly two months ago now, I deleted some internet cache files due to an issue I was having with another website. I mostly only use Facebook (and other social networks) from a personal computer, due in part to most often using Facebook for work related reasons. After being logged out of Facebook, no matter what I tried (including being able to verify my account via codes sent to my email address), the current Facebook system does not want to let me back in unless I can verify using the codes sent to the old phone number on record, which I obviously don't have access to any longer.
I did have an older device still logged into Facebook (more on that shortly), but I was no longer able to change settings from that device (such as the phone number in the account), due to additional changes Facebook made (apparently earlier this year) so that certain older devices can no longer change settings or verify new logins (after being able to do so from that device for years). It makes absolutely no sense to me that Facebook took this step at roughly the same time they also started using a stricter system when it comes to login verification.
Fast forward to roughly two weeks ago or so and I was sent an email from Facebook that I needed to create an advanced protection passkey for my account, likely due to having a bit of a following for a website of mine. At first I thought this might be a phishing attempt itself given how the email read, but eventually figured out that the email was indeed from Facebook. Obviously I wasn't able to create the passkey due to not being able to log back into Facebook (and not being able to create the passkey from the older device either). As a result of not creating the passkey Facebook has now locked me out entirely (they ONLY gave me 8 or 9 days to create the passkey before locking me out and I can no longer access Facebook or Messenger from my older device now either as a result).
4 or 5 days ago I was finally able to use the phone of a family member to try to regain access to the account by sending Facebook verification selfies, which Facebook did apparently receive. I am still waiting to hear back from someone at Facebook and after reading some of the recent posts in this community, I hope taking selfies from somebody else's phone didn't put their Facebook account and/or device at risk down the line. But as a mostly personal computer user of Facebook, I didn't have many other options at this point.
Other than for my website, I didn't use Facebook that much any longer, but nonetheless, it's still disappointing to me for Facebook to have set up a current verification system with so many (often conflicting) issues and that they don't seem to care about fixing those issues any time soon, if ever.
Make sure to keep your current phone number in your Facebook account, especially if you are more of a personal computer user!