Gents, I think there is more to it that meets the eye. Please watch this news item. Will answer a lot of question.
The issue is not Turkey presence in Afghanistan, rather the NATO flag that it might be under. I sense there is something going on at the background with Chinese pulling the strings, which I am ok with.
Hungary has been a Turkish ally, somewhat. The reason Turkey is asking for Hungarian help is because they're close diplomatically, and because they have more experience in Afghanistan than Turkey.
This has nothing to do with China. This has everything to do with NATO. NATO knows Turkey has good diplomatic relations with Pakistan, wants to exploit that, and is probably pushing Turkey to become the neutral military presence at Kabul airport.
Kabul Airport is very important for NATO. It's a civilian airport with the most developed infrastructure in Afghanistan. So it cannot be shut down as part of the deal and it has good capacity to handle military logistics.
Should things go south, NATO wants to keep a door open to land back in Afghanistan. If they don't have Kabul airport, their only entry back into Afghanistan will be through Pakistan, and we don't want to be on the receiving end of that pressure.
If NATO, Pakistan can hold and keep secure, neutral control of the airport, it's in our i interests. We don't want them to come back but to ensure that the Afghan Taliban must work together in an all-inclusive Afghan only government, so this airport will be a deterrent for militant takeover by the Afghan Taliban. If we don't have the airport, Afghan Taliban might resort to militant takeover prompting NATO pressure on Pakistan to provide a passage. In such a case, if we don't, we lose... and if we do, we still lose as we could find a new enemy on the west.
Don't repeat this mistake from the start of the War on Terror.