iMac started scrolling uncontrollably to bottom of webpage. Mouse has been replaced still happens.

Since swapping the Magic Mouse didn't help and the problem still happens after a few minutes on a page, we’re likely looking at either a software/service-level issue or a rogue input device acting up in the background.

I'd suggest starting by ruling out any input device conflicts. macOS can get confused if multiple input devices are active.

1. Go to System Settings > Bluetooth, and remove *any* old input devices (especially third-party ones or another mouse/trackpad).
2. Disconnect any external USB keyboards, mice, or dongles temporarily. If you’re using any third-party pointing device software (like SteerMouse, BetterTouchTool, Logitech Options, etc.), try disabling or uninstalling it.

Next, check your Mac's Accessibility settings. There might be an accessibility setting that’s misfiring or being triggered unintentionally.

1. Go to System Settings > Accessibility > Pointer Control, and make sure Scrolling isn’t set to behave strangely or use alternative keys.
2. Under Keyboard > Accessibility, make sure Sticky Keys or Mouse Keys are off.

If neither of those helped, I suggest creating a new user account on your Mac. Log out of the current account, and then, log back in with the new account. If that resolves the issue, it will be something amiss with your current account.

Next, try Safe Mode to see if that helps. Safe Mode disables login items, third-party extensions, and caches

Ref: Use safe mode on your Mac - Apple Support

If it doesn't help, that would confirm the issue is likely related to a background process, extension, or cache corruption.

Does that behavior occur only while browsing web pages, and if so, is the behavior occurring in Safari?

It seems to me if you exhaustively performed all the steps described by Tesserax, and the problem has persisted, then a trip to the Genius Bar is in order.