There was an Insider update, so while I was signed into that copy of Windows I decided to setup Outlook [don't ask me why]. Much impolite language followed. Since I was running an Insider version of Win11, and that *might* conceivably have been the fault, I repeated setting everything up in a test copy of Win11 with the same results, so at least with today's versions, what I found *might* be helpful to someone else.
I'll start with Gmail, since it's hugely popular. To set up a Gmail account, the New Outlook opens the default browser and has you sign in. Then once you're signed in it switches back to Outlook, with a message window asking if you want the browser to open Outlook. Click OK and it switches back to Outlook, with the setup window saying it's waiting on the provider, staying that way for quite a while until it finally says it failed. Trying again, multiple times, got the same results. What worked was installing Chrome, signing in during setup, and setting it as the default browser [you can revert back to whatever browser you like afterward]. Outlook then opens Chrome, and when it switches back to Outlook it works.
I have a secondary Microsoft account [outlook[.]com] that's not tied to any copy of Windows. Adding it to Outlook should be super easy to say the least, but here the problem was that Microsoft asked for everything but the password, and nothing else worked. After multiple failures the setup window Finally showed other ways to sign in -- clicked that and the password option appeared, which of course worked like it should.
And I have an email account using a domain we own. Setting up a run-of-the-mill IMAP account should be easy, and the Outlook account setup filled in all of the blanks correctly. But of course it would not work, reporting many, many times that it failed. The trick was when I got to the setup window where you add your password, turn the switch on to show more. That shows you all the settings, including a space to add the password again, and that's what got that account working.