I know @lkjkfjlifjsdf already knows how to do that, but for future visitors stumbling upon this problem: I have posted a short bash command that extracts the URLs from appstate.bin
It still contains more urls than it should, I think, but I can live with 40 additional urls in a set of 240 actual urls.
strings appstate.bin | \
grep -v -e 'operaui://startpage' -e 'Speed Dial' | \
grep -A2 reader_mode_state | \
sort -u | grep -v 'reader_mode_state' | grep -oh "http.*$"