Yeah supporting Microsoft for login seems rather convoluted!
I’ve just walked through it and we’ll have to update our documentation. It does require a free Azure account as you noted.
You then have to register a new application in Microsoft Entra ID. This required a credit card as you mentioned. I was able to configure this and get it working for login and have not been charged (be sure to select the web option instead of single-page application). There are subscription plans for Microsoft Entra but you do not appear to need those.
For Facebook, you need to go to https://developers.facebook.com/async/registration — I hit a wall on this because it’s requiring me to have a Facebook account older than 1 hour to continue. So I can come back to it.
Update: made it through the Facebook flow but couldn’t activate login without “verifying as a business”, which requires uploading documentation. I’m not going to do that, so I can’t complete the process.
Neither option seems to require payment.