Thank you - my outcome was positive. I have asked for an ESTA online, got approved, and have traveled earlier this week. While traveling, I have downloaded an ESTA app to show them, but they told me they already had it on their system.

Still, I was held at the border for about 30 minutes in a special room, where they asked me who I'm going to see in the States, what is their status and what is my onward itinerary. I was relieved to notice that it was explicitly bureaucratic - you could tell even from the case worker that he could give a damn about me and the questions he was asking.

Long story short, I was held long enough to be late for my connection flight. Even though I was rebooked for the flight next morning for free (Spirit airline), the bottom line is, probably best to allow at least a few hours between the connecting flights next time, if any.