Help! V slow MacBook Air (2017) after Monterey 12.7.1 update. Fan goes mad

Have you tried to boot the MacBook in the safe mode to see if the issue persists? If it does not persist in the safe mode, it is caused by an external piece of software, then you might want to evaluate the software installed to your mac

Start up your Intel-based Mac in safe mode

1. Turn on or restart your Mac, then immediately press and hold the Shift key until you see the login window.
2. Log in to your Mac.
3. You might be asked to log in again.
4. On either the first or second login window, you should see “Safe Boot” in the menu bar.

It sounds like you have a runaway process - some application running in the background slowing the computer. I like to start with the Activity Monitor to see if I can identify the miscreant. Launch Activity Monitor (it’s in the Utilities folder) and click on the 2nd column (% cpu) so that the processes are sorted according to how much of the CPU cycles they are using. When the computer is operating normally you shouldn’t see any process running faster than about 40% and that would be a momentary blip, not constant. For example, right now all my processes are running at 20% or lower except for the WindowServer that jumps up in response to my switching from one window to another. If you see a process consistently high, that’s your culprit. Identify what it belongs to and see if there was a recent update that you missed. It could be that simple.

If it is fine in safe mode, it is caused by external software, that much you've discovered now. What I would do is boot normal again, and then boot up activity monitor (type activity monitor in launchpad) to see what app is using up much resources. Then after that you can delete that specific app.

Do you have a virusscanner installed? That kind of software is mostly the culprit by this kind of things