I'm just and old retired guy running Windows 10 Home on an old Asus computer. So, take my comments with a grain of salt.
I had this same issue. I don't know why Microsoft keeps unnecessarily changing things during updates. It likely is unintentional, but t's quite frustrating. My solution was to disable the Microsoft Exchange Add-in. If you need the Add-in, this fix won't work for you.
I believe the password request is for a Microsoft Exchange password, which is different than my Microsoft password and I have no idea what it is. Unfortunately, there is not a "forgot password" link in the dialogue box that pops up to allow you to reset the password.
Open Outlook
Click on File
Click on Manage Com Add-Ins
Under Microsoft Exchange Add-Ins, Click on Disable this Add-In
I tried this and it seems to have worked for me. I no longer get the request for a password and Outlook opens much faster.
I hope this helps others. If not, good luck getting a concise and helpful response from Microsoft Support. It's not that they don't want to help. They just don't work with the old versions of Windows, especially on older computers, and when there is a bug in an update, they don't experience the issue and consequently don't know how to fix it because they've never had to do so. I wish they would set up some legacy systems for some of their technical support to use full-time, so they would understand the issues.
As a side note to those of you that are getting frustrated with how your older computers keep getting slower, I have found that using Razer Cortex, which is free to download and use, really speeds up my computer. This is also good software for gamers. It takes a while to download, and it loads somewhat slowly in the background during startup. Once it loads though, you can select System Clean under the System Booster tab. I run this periodically and my computer is usually faster after doing so. Be patient the first time you use it. It might help to clean one set of files at a time, saving Backup Files until last.