Sorry, this is going to be a rather long answer on my favourite non-topic.
I am readily willing to accept that there is a correlation between change of air pressure and fish activity. I am as certain as I can be that change in pressure does not CAUSE that change in activity. It is vital to understand the difference between cause and correlation.
Science shows that a change in air pressure (atmospheric pressure) causes a corresponding change in pressure in the water (hydrostatic pressure). If you do the maths, a change in atmospheric pressure caused by a typical storm event only causes a small change in hydrostatic pressure equivalent to a few centimetres of water column.
What this means is that, even if a carp could detect that small change in hydrostatic pressure, it could not tell the difference between that change and a change caused by swimming a centimetre or two deeper or shallower.
Let me give you a true analogy. I live in a remote village in rural France with a very poor internet connection. I observed (the correlation) that, every time it rained, our connection became so slow it was unusable. It seemed obvious that the rain water was getting in somewhere and I spent a lot of time checking everything in the house to try and locate the problem. I eventually gave up and called out the telephone engineer.
I explained the problem to him and he just laughed. He said he did not need to do anything. Every time it rains, the kids in the village go inside and watch Netflix. This takes up all the limited bandwidth that is available. That is the problem.
Then he gave me his call-out bill!
So understanding the CAUSE is vital to interpreting the CORRELATION. Atmospheric changes cause all sorts of changes in wind, temperature, lighting etc. etc. And more importantly these may differ according to where you are. So what is true for say Essex is not necessarily true for mainland France where, in Summer, high pressure seems to dominate all the time.
In France I have had some spectacular catches with high pressure, bright sun, high temperature and no wind. Best tip is to ignore pressure and watch what the locals do. It may not improve your catches but you will have some cracking barbeques 😉.