It’s more than cookies. I’ve had it between group of us checking flight prices, all different PCs, IP address and browsers, and the prices were hiking up. Likewise on booking. Best to have one person checking and booking.
Basically prices can go up with perceived demand. Doesn’t always though, and depends on airline.
Comparison sites will have their cut within the price.
Remember, cheapest flight tickets may have catches. No luggage allowance included so have to pay extra, taxes and booking fees extra, restricted seat choices and get stuck by the toilet etc.
On comparison and having to take hold luggage (bike, skis etc), I’ve found overall price can sometimes work out same as a cheap BA flight. More so if the budget flight means going to some far flung airport and thus factor in cost of getting there.