Stopover with Turkish Airlines in Istanbul

I'm sure James E will be along any minute to regale you with the merits of Turkish Air. If not, you could PM him.

Yes, 3-4 times. It's well worth it, although it was more valuable to me after I spent considerable time in Istanbul on a separate trip. A 2-3 day layover stint just isn't enough to see much in Istanbul, but it's a great way to "fill in the gaps" once you're already familiar with the city. I can always find something to see that I haven't on prior trips. Iceland Air has a similar stopover although the number of maximum days is longer, I believe 3 versus 7 or so). To me, it's like getting two-countries-for-one, and that's why I fly Turkish Air to Europe even though it involves a detour in Istanbul. There is a Turkish VISA involved when leaving the airport for sight-seeing, but that's a minor cost in the grand scheme of things.

A1) Here I am and yes its a pretty "okay" airline 🤣
A2) Almost all of my flights to Europe are on Turkish Air and from time to time I will spend a few days in Istanbul on my layover; but I have never used a "plan" or "offer", when booking my flight the cost has always been the same if I do a 2 hour connection or a 3 day connection.
A3) Its been almost a year since the last time I did it, maybe things have changed.
A4) Another thing that has worked for me is using Turkish Air in open jaw flights to save a bit of money and get to visit a new place.
A5) Houston to Budapest Round trip generally costs more than an open jaw Houston to Podgorica, Montenegro (or any of hundreds of other routes) and then Budapest to Houston
A6) Last year my Houston to Kyiv (changing in Istanbul --- as do all Turkish Air flights) then Istanbul to Houston was less expensive than my daughter's Houston to Istanbul round trip (we traveled the same flights to and from Istanbul).

OP may be referring to the "stopover" option for a free night in a hotel, or a free guided city tour (your option depends on the time of your layover -- hotel for those with an overnight layover, city tour for those with a long daytime layover).

IIRC, I believe these amenities were only offered for business class passengers, with some other qualifications (entire itinerary on Turkish Airlines, layover of at least X hours but less than Y hours, etc.).

This is from memory, from pre-COVID times, so things may have changed (and my memory is not infallible). I have not taken advantage of the free hotel/tour benefit personally -- though I remember it had been widely praised as surprisingly generous and worthwhile (the hotel was not some low-end flea-bag, and the city tour was said to be a nice way to get a quick taste of some of the city's sights on a quick stop -- it's hard to imagine an airline offering such a generous benefit, but they did; maybe they still do).

If you are just talking about a "stopover" in Istanbul -- days in the city -- then most airlines offer that, as long as you book your ticket that way. I have a "stopover" of 5 days in Istanbul booked for next October, on a complex routing in business class booked with United Airlines points, coming from USA to Istanbul, then continuing onward to Malta after 5 days in the city (booked as a "multi-city" trip, outbound, intermediate stops, and return).

Hope that helps (and if the question is about something else, or if I've got the details completely wrong, please ignore this and accept my apologies).