Have hedge funds tried to use web search data to predict stock movements?

It’s possible, but don’t think it would make sense as the idea is to “separate the signal from the noise”. Web search data by definition is already several days old by the time Google finds it and you would be making buying / selling signals off old data that is days/weeks/months old that the market had already priced into the stock.

Most algos that use a sentiment strategy extract sentiment for “breaking news” from credible sources like Bloomberg & Reuters. That’s why if content has an incorrect ticker symbol (BAC vs BA) it causes temporary price spikes in the wrong stock due the typo that caused increased volume.