I'd first try removing the auxiliary drive belt and turning every pulley and ancillary ( power steering pump , alternator etc) by hand. All should turn easily (with the exception of the AC pump) with no grittyness or wobbly pulleys- If you do find a sticky pump / alternator then it should be replaced or repaired
If the engine is stone cold you can briefly run it with no belts to see if the noise changes or has gone away, this will help show if an ancillary is the issue
If this is OK then its possibly an airleak after the airflow meter, any air dragged in here isn't 'seen' by the ECU and so not compensated for and can lean the engine out and can also allow the engine to rev up when not desired causing rough running.
As its a mechanical fault it tends not to turn on the fault light and you can sometimes hear a 'hissing' noise with the engine running.
Check the hose clips for tightness and inspect the trunking for any cracks or splits and also all the vacuum system, the small bore pipes and fittings for cracks and missing parts.
The best way to locate a leak is to have the engine running and warm and then spray lighter gas /propane or brake cleaner around each joint in turn. If the engine rev's up you've found your leak.
Now you might think that spraying lighter gas around a hot engine isn’t wise, however the flash /ignition point of gas is about 400°C so you need a naked flame or spark to set it off and I’ve used this method for many years without incident.
Work your way through each possible joint one at a time and you should find it. I use a slightly flattened piece of brake pipe and some rubber hose from the can of lighter gas to provide a spraying 'wand' and allow a direct blast of gas into each area, especially those difficult to reach with large implements.
a blocked cat is a possibility but I'd still check what I've suggested 1st as its a lot cheaper to replace a pulley or repair an air leak
a new cat is about £600 and an hours labour to fit whereas repairing a vacuum / air leak can sometimes require no parts an a hours labour