Just to make sure I understand you correctly, you changed your Hotmail/Mcrosoft password and now Outlook '2010 is asking you to enter the password for the account - is that correct?
Just going over your original post again, when you changed the password, you can use the new password to log into your computer correct?
I want to be very careful about what I suggest here since I've run into a situation where I was unable to add an Outlook.com account back to '2010 after it stopped working. Had another person report the exact same thing happened to him. Unfortunately, Outlook '2010 is out of support so there is nothing that can be done about anything if it's a '2010 issue. I don't have that test system handy to see if the issue still exists.
With that said, a quick test would be to create a new Outlook profile and configure the Outlook.com account using the Control Panel Mail app to see if the Hotmail account gets configured. If it doesn't there's nothing that can be done about it, at least in terms of adding it as an Exchange account
a) - With Outlook closed open the Control Panel <Mail> app
Just in case you need info regarding how to access the Control Panel Mail app, that's described in the following article by Outlook MVP Diane Poremsky
Where is the Control Panel Mail icon?
https://www.slipstick.com/how-to-outlook/where-...
If using Windows 11
How to Open Control Panel in Windows 11
https://www.lifewire.com/open-control-panel-in-...
b) - Select <Show Profile> --> <Add> --> give the new profile a name (no need to remove the existing Outlook profile)
c) - Configure your email account(s)
d) - Set the newly created Outlook profile as the default for the next time Outlook is opened otherwise it'll use the old profile
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