Print code-fenced sections of a Markdown document
While your code looks ok, it could be improved greatly by making use of RS (record separator) and NR number of record, provided you're using GNU awk.

 awk -v RS='```[a-z]*\n' '(NR+1)%2' file


In this case RS is set such that it is catching everything between triple backticks with optional text.

The only awk statement is to print one record out of two.