If your computer won't restart after installing Windows Update, you will have to boot into Advanced Options (WinRE) screen and take any one of these steps.

If Windows 11/10 is stuck on Restarting screen and not restarting properly after Update, Blue Screen, Black Screen or at any time, then see this post for the resolution.

Microsoft has fixed a known issue causing restart loops and taskbar problems on Windows 11 systems after installing the June KB5039302 preview update.

The problem is it seems to be stuck in a loop of displaying the System Settings Change dialog box with "To finish setting up your new hardware, you must restart your computer".