From the available public info, Gakuran appears to have these fighting styles: Boxing, Muay Thai, and Hakari.

A few notes:

  • That list comes from a recent gameplay video showing the style reroll menu.
  • A separate recent guide also describes Gakuran’s combat as a melee system built around punches, slams, stomps, and reactive movement rather than a huge style roster.
  • I couldn’t verify any official full style list from a primary game page in the info available here, so this is the safest current answer.

If you want, I can also help sort out whether those are the only styles or just the ones unlocked so far.