How long will an airline delay a flight for late checked-in passengers on an international flight?

I once worked gates and check-in for a major airline at JFK. The IATA rules are the same everywhere, but culture/airline staff is different depending on where you are.
You might have less time if Turkish is usually this good on-time: https://www.flightstats.com/v2/flight-ontime-performance-rating/TK/52/IST

Seems you would only have minutes to spare, perhaps 10 or 15. They check the boarding progress constantly so that they can make those “Mr. Smith, please get to gate xx, final boarding” announcements BEFORE any actual, expensive departure delay occurs where they will be fined (“departure” = pushback from the gate/off-block time). So you would have to start counting the “delay” from the time your name would be announced over the public address system, until the moment your bags were removed and the pilot was notified of the confirmed passenger manifest/door closed. Even LESS time if you are in the last boarding group to be called (if boarding by row) because they wouldn’t notice you were missing right away.

It depends entirely on the country and airline’s attitude to punctuality, which passengers were delayed (international? domestic? high-fare? low-fare? frequent-flier status?), how many (2? 100?), whether their delay was foreseeable (e.g. immigration) or just dawdling in the departure area. Also how security-conscious the airport is, and how expensive a gate is and delay compensation (if the next flight at gate is delayed). Assuming they’d checked in of course.

One extreme example:
In 2013 was in the Philippines, flying on Cebu Pacific Airlines (a low-budget carrier) from Cebu (domestic I think). There were about ~14 Korean tourists (business class). Everyone else got on on time. The Koreans were still in the restaurant or souvenir store, taking their time, knowing they were holding things up and not caring. But the staff didn’t close the doors or announce any delay. They just silently held the flight (for 40 min) until the Koreans finally decided to come. No apology, no nothing. After 25 min I had asked the FA why could they not just close the doors and depart. She didn’t give me an answer. I said if they’d told us, I could have used an extra 40min in the souvenir store myself.

Flight delay compensation in the Philippines and SE Asia is not strict like EU and US.

Not at all. This is a scheduling matter and any delay is likely to cause them issue as most airlines run a tight operation. They do a last call but your luggage will be removed as soon as they can once they decide that the gate is closing.

This is even the case if you are delayed by their own fault. Several times I had connecting flights that were delayed and arrived at the gate within 5 minutes of closing and was simply advised that that was the scheduled time and that was it. Instead of keeping the door open a few minutes, they preferred to schedule me and dozens of other passengers on future flights.

If they do delay the flight for a passenger, consider yourself lucky. Maybe the plane is not going further that day and they count that other passengers do not have any connections later but that would be the rare exception. Remember that in your example, they had no idea you were going to make it, so there is little chance them to be expecting you, as opposed to them knowing you are on the incoming flight for a connection.

In the case where you have already checked-in, they will make several calls in the terminal since, as you said, they do not know you left. They will rarely delay the departure even in that case and not by more than a few minutes, it could be too costly for them.

Where positive passenger bag matching is the policy, the process of locating your bag and offloading it begins some time before scheduled departure.

By most airline policies, you are required to be at the gate ready to board at least ten to fifteen minutes prior to scheduled departure. At that time, once the gate agents have scanned the boarding passes of everyone in the waiting area, they will be able to identify no-shows, and begin giving away their seats to standby passengers.

Around the same time, the ramp agent will begin tracking down any bags that those no-shows have checked, and may begin off-loading them. This does not take as long as you might think, and in fact might be faster on a larger plane of the sort typically used on intercontinental flights; the bags are scanned when placed in loading bins, so the handlers will know exactly which bin(s) to check for the bags.

On domestic U.S. flights, positive passenger bag matching is no longer required, as all luggage is inspected by the TSA. As such, the most likely scenario is that the flight would simply depart without you with your bag still on it, its final disposition dependent on your final disposition.

Eventually, and this won’t take that long, they will remove your bags and the flight will depart without you. I have had this happen on a couple of flights. The airline may be slightly more patient about doing this on the last flight of the night, if it’s not going to impact any other operations, but they won’t wait forever.

Personally I doubt most airlines would wait more than 15 minutes or so, unless you were a very, very good customer of theirs or your group comprised a significant amount of the passengers on the flight (e.g. 8 passengers out of 50 seats). Remember, they’re making the other passengers unhappy by waiting for you.