When running a search on the website, would the search words count as "tracking", meaning that a user would need to have been informed that search activity would be tracked (a line on the cookie banner etc).
I'm not sure what is considered as tracking these days and it's unclear whether search queries count as one of those things.
My point here is that if this were to be the case, that would effect the cookie banner and the consent forms to allow that sort of tracking to take place, assuming consent is required at all.
Also on the plus side, if the model works, you can use that to provide your customers with a lot of power and a seamless experience.