After an update Microsoft may force you to do a "setup" process. Part of this will end you up in a screen forcing you to either log in with a Microsoft account or create one. It does not give you an option to keep logging in with a local account.

How To Escape: 

At the end of the process it has a screen that forces you to log in using an MS account or to create one if you don't have one. There is nothing on the screen to go past it. However if you back up a step it brings up a new screen ( as shown below) which lets you skip for now.

If you cant get this, 

If You're Completely Locked Out:

Boot to Safe Mode:

• Restart while holding Shift, or force restart 3 times to trigger recovery
• Navigate to Troubleshoot > Advanced Options > Startup Settings
• Choose Safe Mode and try logging in with your previous local account credentials

Create a new local account: You can create another local account to use as an alternative through Computer Management or Command Prompt (if accessible)

How to Prevent The Setup Process:

If You're Getting Persistent Microsoft Account Prompts:

Disable "Let's finish setting up your device" screens: This is a common "second-chance out of box experience" (SCOOBE) that appears after feature updates Change From a Local Account to a Microsoft Account in Windows - Microsoft Support. You can disable it through:

• Settings > System > Notifications > Turn off "Suggest ways I can finish setting up my device"
• Or via Registry: Navigate to HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\UserProfileEngagement and set ScoobeSystemSettingEnabled to 0
• (Registry entry attached to this FAQ)

If You Need to Switch Back to a Local Account:

From Settings (if you can still access your account): Go to Settings > Accounts > Your info, and click "Sign in with a local account instead" windows 10 - How to login without Microsoft account after update - Super User

Alternative method:

• Press Windows + R, type netplwiz, press Enter
• Uncheck "Users must enter a user name and password to use this computer"
• Apply and restart

Prevent Future Issues:

Disable Account Suggestions:

• Settings > Accounts > Sign-in options
• Turn off "Use my sign-in info to automatically finish setting up after an update"
• Disable "Show account details like my email address on the sign-in screen"

Registry Method for Persistent Popups: If you're getting fullscreen popups asking to use an online account with "remind me in 3 days" options if i upgrade to Windows 11, am i forced to use my MS account to login to my computer - Microsoft Q&A, you can disable these through Group Policy Editor:

• Run gpedit.msc
• Navigate to Computer Configuration > Administrative Templates > Windows Components > Cloud Content
• Enable "Turn off Microsoft consumer experiences"

The key is that you are not obligated to use a Microsoft Account if you do not wish to, despite Microsoft's increasingly aggressive prompts. These methods should help you maintain your preferred local account setup.