I came to Ukraine in May 2021 and left in early December from Kyiv. So I overstayed my 90-day visa-free duration.
At the airport when the immigration staff realized I overstayed, he took me out of the queue and made me wait outside of a room. Several others were also waiting there. After about 1/2 hour, I was called into the room and asked to pay. No other useless questions as you have read online. I paid and THAT WAS IT! I guess it's very common that an American overstays because the staff there said to me, "see you soon" when he handed back my credit card. Another clue is when I joined a virtual town hall meeting hosted by the U.S. embassy a few weeks earlier, the embassy staff brought up the subject. She was VERY CASUAL and advised the attendees to keep the receipt after paying the fine just in case someone goofs and
doesn't clear us.
I have heard too that you can pay in advance at a government office. When I discussed it with my attorney, he advised me to simply pay it at the airport. "Everyone did it this way", he said.
They don't purposely keep you waiting at the airport for hours. It can be hours if they are busy, ie. you show up at the same time with a bunch of overstayers! So I would advise you to give yourself two extra hours at the airport just in case. I waited 1/2 hour while 2 other people were also waiting.
In theory, one has 15-days to pay the fine. When I asked the lady there what difference it makes if I pay on the spot or a few days later. She replied, "if you try to re-enter Ukraine before it's paid, it can be an issue". Although by law as long as 15-day isn't up yet, they cannot stop me from re-entering, provided I meet all other requirements for entry, knowing in Ukraine rules are often the words of the guy in charge rather than what is on paper, I simply paid on the spot. It's not like I would get a discount if I delay it. By the way, if you don't pay up in 15-days, you will receive a lifetime ban from entering Ukraine!
So I left for Moldova and got a new Ukrainian visa there the next day. I was back in Ukraine that evening.
Keep in mind that an American passport grants you to stay in Ukraine WITHOUT a visa for 90 days out of every 180 days. I have heard online that some folks are allowed back in before waiting for a full 90-days outside, but do you want to play this visa "roulette"? There is no guarantee here. On the other hand, if you have overstayed, it's unlikely any immigration man would play nice and let you back in without waiting for a full 90-days.
I was back in Ukraine in 24-hours even though I overstayed because I got a REAL visa this time.
Lastly, overstay is no big deal only for certain passports with American being one of them. I've heard an Indian passport can get you banned for life simply after only one overstay!