24 visa-free transit - Shenzhen Airport

Tobias, I will try to be very clear.

When traveling on 24 hour visa free transit, you have absolute right to travel via two or more airports within mainland China regardless of your citizenship as long as your total travel/transit time is not longer than 24 hours counting from your firsts scheduled landing in China (in your case in Beijing) until your final departure from China (in your case from Shenzhen).

So, if your itinerary is in compliance with this rule you are fine regardless if your first landing is Beijing or Shenzhen. Also, Shenzhen is still eligible airport for 24 hour visa free transit and you do not have to worry about.

When you land in China for the first time, being it Beijing or Shenzhen, the first thing you will do is to approach 24/144 hour transit counter where you will apply for a temporary entry permit. This is absolutely free of any charge. Here you will present your flight tickets (it is advisable to have them at had as printouts to speed up the process) and after a short check, you will be granted the permit. Having a permit, you will cross the immigration because your next flight will be a domestic one. There is nothing problematic here because all the flights between two Chinese airports are domestic and this is the reason why do you need a permit.

When you arrive at your second destination within mainland China, you will just cross the immigration and proceed to the gate with your flight out of China.

I hope this explanation clarifies things and brings some peace of mind.