They can track it with a simple js onclick handler, or a simple redirect on their server, that's not the problem. (They do both btw.) The problem is that they want to track what I do on the links I already clicked - which is absolutely none of their business.

Perhaps so, but I still find it highly objectionable.

Just search in a private window then, the part of the tracking that I assume you find objectionable (gathering info on what sites the current user visits) goes away when you close the window while the part that helps the search engine (and thus results in better search results for everyone) still works.

Now sure, we can argue that maybe the company should provide options where you can say "you can use what I click on for search training but not for targeted advertising" (I think Google does provide a set of options that pretty much disable all web history/targeted ad collection), assuming you believe they follow through. But the company needs to pay for its services somehow so I can't blame them for tying the two types of tracking together, I still have tools as a user (private window) to avoid it if I care enough to.