Like many others I am experiencing the issue of being told too many attempts with the incorrect password have been made, and then the captcha also just looping and not fulfilling, while then also being told the verification method isn't currently working when attempting to use 2FA.
I have reached out to customer support live chat via a separate account (as it requires being logged in to use), and explained the situation to them.
This was escalated to a higher up within the chat, that queried if I had attempted to log in several times. I mentioned I had during the initial outage, as I didn't realise there was initially an outage.
They informed me that the account gets locked for 24-48 hours from the last login attempt, so in this case the solution is to not continue attempting to log in and instead to wait 48 hours.
So in this case it appears the issue is potentially that peoples accounts are temporarily locked for 24-48 hours, and continuing to not make progress when attempting to log in due to the above.
This is why some people are seeing progress occasionally - they are likely attempting to log in for the first time in 24 hours.