jq '.[]["songs"][].file | match("\\.([^.]+)$") | .captures[0].string' songs.json -r  | sort | uniq -c | sort -nr

  3169 xm
  1011 mod
   226 it
    86 s3m
     4 nsf
     3 rad
     2 amd
     2 S3M
     1 mtm