Are you new to Mac? When you are in a browser, the cursor will change to a pointing finger when it's over a link, but only if the browser if the active application. You might see the browser window but have another application in the foreground (you would see the name of the active application in the menu bar). If that were the case, the pointer would remain an arrow.
What you describe, if it persists, is most likely due to a software preference somewhere. It could be in system preferences, or your browser's application preferences. It is not a bug and it is not the operating system. If your computer boots, you know that Monterey is bit for bit perfect. That's the way the signed and sealed macOS works.