Two separate flight tickets

Tom, it is perfectly eligible to have two separate tickets. Single ticket with the landing in China was never a condition in order to be eligible for 144 hour visa free transit. So, having separate tickets and flying on unrelated airlines is fine. The main detail that has to be fulfilled is that the immediate point before and after your mainland Chinese destination are located in two different countries or eligible territories (eligible territories: Hong Kong, Taiwan and Macau).

You example of Seoul - Chengdu and later Chengdu - Prague is definitely eligible and you can use two unrelated tickets. However, I have to warn you that there is no direct (nonstop) flight between Chengdu and Prague, so you will have to take care that your segment, Chengdu - Prague does not have any additional landing within mainland China because under 144 hour visa free transit, you cannot have two mainland Chinese airports in a row. Again, take care about immediate points that I have explained in the initial part of this post and you will be perfectly fine.