How can I effectively block Windows Store and its apps?

Have you tried setting the registry key "windowsStoreRequirePrivateStoreOnly"? This could limit access to only apps from your corporate environment.

If your primary concern is Quick Assist, you can disable it for your organization using specific policies. Check out the Microsoft documentation on disabling Quick Assist, and also consider adjusting the settings for Remote Assistance through Group Policy. However, if you're aiming to block the Windows Store altogether, you'll likely need to implement software restrictions to prevent any user-level installs.

You might also consider enabling installation strictly from the company store. While the company store doesn't exist anymore, that policy can still be applied.

To block users from installing packaged apps, you should use Group Policy to disable installations for .msi and .appx files. Windows Store apps have a level of trust, so you’ll definitely want to disable that feature. Applocker can also be a useful tool here, particularly the BlockNonAdminUserInstall policy to keep users from installing apps.

Disabling downloads from the store is generally not recommended, as many important apps update through it. Regarding Quick Assist, remember that while it used to need admin rights for installation, some store apps don’t, so it might be helpful to look at blocking other remote access tools too, like TeamViewer or Rust Desk.