How to split a text with several headings and subsequent text into two columns using postgresql?

My test looks as follows: I have several text pieces with a one-line header introduced by a '>'. It is not clear which kind of text appears in the header, only that it is just one line. The length of the text piece after the header can vary. Also there might be empty lines inbetween as shown between text parts one and two (see below). Also the number of text pieces is variable.My test looks as follows: I have several text p