Apple has a search engine, it’s just not publicly accessible. They’ve had a web crawler for many years and their internal search engine is likely what powers things like siri suggested sites and information for apple maps. It is correct they could enter the search and advertising game at any moment, though unlikely because it would destroy their brand integrity.

That said apple is no saint for privacy. For one they actively enable google; they take billions from google to fund safari development in exchange for prioritizing google as built in search and feeding google user data. For a company like Mozilla this is an ethical conundrum; without googles money they’d likely be done. For a company like apple it is inexcusable. the few billion, while a tremendous amount (I think 18 billion?) is a pittance to them.

Further to your point of “active permission” with the tracking limiter this is not always the case. Apple is aware and does not do anything to reform. Part of the reason companies want you to use their app on ios is because then you will be far more likely to open links via the in app browser, which is still safari/webkit, but now escapes sandboxing and allows for far more precise tracking and fingerprinting even if you utilize the tracking limitations built into ios.

Notice how only sketchy games with tons of blatant ads will prompt the “ask ad not to track” box. Instagram, twitter, youtube, reddit, etc generally don’t because they don’t need to track you through permitted routes. Apple has long been aware of this and continue to do nothing (forcing links to open in safari or another browser, limiting traffic on in app browsers, etc). Lord knows what other tricks scumbags like facebook have to circumvent systems and track everything you do. Apple is well aware it happens without user consent but tolerates it and then has the gall to say their hardware and software is “privacy oriented”