My monitor spikes hardest when I cook and the extractor seems to do nothing - is the hood the problem?

Your hood is very likely recirculating, and that would explain exactly what you are seeing.

There are two kinds and they look identical from the front:

Ducted. Pulls air through and pushes it outside through a pipe. Removes everything - particles, moisture, smells, combustion products.

Recirculating. Pulls air through a charcoal filter and blows it back into the room. Removes some smell. Removes essentially no particulates and no moisture. Very common in flats where there is no external wall route, and it is the default on a lot of cheap installations.

How to tell in thirty seconds: look at the top of the unit. A pipe going into the wall or ceiling means ducted. Vents on the front or top of the hood blowing back at you means recirculating. Also hold a tissue near the outlet while it runs.

If it is recirculating, it is doing what it was designed to do, and it was never going to move your particulate reading.

If it is ducted and still doing nothing, the usual causes are a greased-up filter that has never been cleaned, a flap in the duct that is stuck closed, a duct that is crushed or far too long, or a fan far too weak for the run. All are checkable and the filter is the most likely.

You are right that this is a source problem rather than a filtration problem, and your instinct to check before buying is worth honouring.

Cooking is the largest indoor source of fine particles in most homes by a wide margin, and frying is the worst case - hot oil aerosolises. In a flat with decent outdoor air, your kitchen is the pollution.

Things that reduce it at the source, roughly in order of effect:

Use the back burners if your hood is over the hob. Capture is dramatically better at the back, because rising plumes at the front escape the capture area entirely. Free, and it is the largest single improvement available to most people.

Turn the hood on before you start and leave it on for fifteen minutes after. Your reading staying elevated for an hour is partly this, you are turning it off while the particles are still in the air.

Lids. Enormously effective and nobody wants to hear it.

Lower heat, less oil, and avoid taking oil to smoking. The smoke point is where the numbers go vertical.

Open a window while frying, even in winter, for ten minutes. Dilution beats filtration for something generated in the room.

On whether to buy the purifier anyway: it is not wasted, it is just second in line.

What a purifier genuinely does well is reduce the background and clear a room after an event. So the useful arrangement is source control while cooking, and a purifier to bring the number down afterwards and to handle the general baseline.

What it does badly is compete with an active source. A purifier running while you fry is trying to filter a room that is being filled faster than it can clean, and that is why people conclude purifiers do nothing.

If you buy one:

Size it for the room using the stated clean air delivery figure, and buy one rated well above the room rather than exactly at it, so it can run on a low quiet setting.

Put it in the room you spend time in, not the kitchen. Kitchen air needs to leave the building, not be filtered.

Budget for filters. The running cost is real and it is the thing that determines whether it is still in use in two years.

And keep the monitor. It is the reason you asked the right question instead of buying the purifier and wondering why the readings did not change - that is a genuinely good outcome for a cheap sensor.