Thanos is obsessed with Tony because they're so much alike
Prop-Tony folks make a big deal about tiny things when they involve Tony. (Just read any content on how Tony "suffers so much" in the MCU.) Tony landing a paper cut on Thanos was lauded as this incredible feat, even in light of Thor practically cutting Thanos in half (though he should have gone for the head). Similarly, the directors mentioning Thanos knowing who Tony is was "evidence" of how important Tony is. Instead, Thanos could have been interested in Tony because he found a kindred spirit, someone just as unconcerned with "collateral damage." After all, Tony was willing to kill an entire city's population (Age of Ultron) and leave half a universe dusted until Tony was reminded of that one kid he exploited and belittled (Endgame). (Note that Thanos is said to have greatly admired Steve's determination during their encounter.)
***
Thanos lounged in the hut on his retirement planet, watching the approaching heroes of the tiny planet that had held the Mind Stone. He noted a particular absence. He asked, "Where is Stark, Death's minion?"
The Soul Stone had revealed to Thanos a true brother in spirit in the one called Stark. A man with an ego as great as Thanos himself. And Stark was even more callous and unconcerned with the effects of his actions on others.
The axe-wielder--Thor--frowned and said, "He didn't come. He told us to hide if we found you."
Thanos frowned and shook his head. He said, "I am disappointed. He and I seemed to share a similar view of the universe and our place in it. I would have called him brother."
The other heroes looked at each other. A woman with white-blonde hair frowned and said, "Honestly, I'm not all that surprised."
Thor nodded and said, "Stark did seem a bit too quick to sacrifice the Sokovians after he unleashed Ultron."
Another blond man firmed his jaw and said, "This is irrelevant. Let's get back on mission." He stepped forward and demanded, "Where are they?"
Thanos paused a moment to remember this man during that final battle. He recalled this man trying to protect his android friend and the Mind Stone buried in the android's head. Unlike Stark, this man held too much concern for other beings to be a kindred spirit. Still, Thanos greatly admired this man's will and determination. So he settled in to answer the question.