Hello
So what you experienced here has two layers to it.
The first layer is your browser seeing the message "managed by org", it really means it adds a policy to allow your device/browser to access your school organization's SharePoint, like it can trust your device/browser. That honestly can stay, no need to get rid of it if you need to continue accessing the school's SharePoint.
The second layer is you actually enrolled your device into the school's Intune so their IT can push group policies for the entire device; hence, you get the password change policy, etc. If you use a org-issued msft 365 account, you might see a popup when initially signing into the app that asked if you allow the organization to access your settings. If you clicked "yes" without much thought, this action enrolled your device in your organization's Intune management. This doesn't mean they can spy on or access your data, but it does allow them to enforce group policies to enhance your device's security. For instance, they might deploy BitLocker, require a more complex PIN, or ensure that your security updates are always current. The rationale is that using the organization's Microsoft 365 apps likely involves working on documents that are property of the organization. In cases such as businesses that need to comply strictly with HIPAA policies, their IT departments can ensure that these devices are secured, protecting them in case they fall into the wrong hands.
What you can do is go to your Windows Settings > Accounts > Access Work or School (note, it is the briefcase icon, not the little person icon). Disconnect the school email listed here. Then restart the computer.
To clear the group policies further, launch Command Prompt in Admin mode again and run the following commands, one at a time. Not all of them will go through completely or find value, and that's ok. Once finished, restart the computer again and see if it works.
reg delete "HKLM\Software\Microsoft\Windows\CurrentVersion\Policies" /f
reg delete "HKLM\Software\Microsoft\WindowsSelfHost" /f
reg delete "HKLM\Software\Policies" /f
reg delete "HKLM\Software\WOW6432Node\Microsoft\Policies" /f
reg delete "HKLM\Software\WOW6432Node\Microsoft\Windows\CurrentVersion\Policies" /f
reg delete "HKLM\SOFTWARE\Policies\Microsoft\Windows Defender" /v DisableAntiSpyware
reg delete "HKCU\Software\Microsoft\Windows\CurrentVersion\Policies" /f
reg delete "HKCU\Software\Microsoft\WindowsSelfHost" /f
reg delete "HKCU\Software\Policies" /f
reg delete "HKLM\Software\Microsoft\Policies" /f