We are now basically at Volume 1 end and there will be no progress in relationship until end of Volume 4 where he accidently touches her boob in yukata during festival, at first he was super apologistic, but then Hime explained how she was happy and scared for first time because MC finally did assert himself and didn't hold back, afterwards they talked about their relationship progress. Funny enough, other characters that gets introduced with each volume gets more interesting development