I wonder if Ariane's mother could quite comprehend Arc's true power only with that duel she completely dominated. All things considered, Arc only probably used 5% of his true power, or rather even less. But then again, she's over 200 years old, pardon me, 170 years, so she ought to have enough wisdom to understand Arc took the duel as a pure swordsmanship thing. She should be able to understand more than Ariane. In the end Ariane hasn't seen anything yet, either, though she does know Arc is versatile.
This did show the difference between hacking and slashing in a game and true skills with a sword. It's surprisingly something not too many isekai bother to address. But then again, if you have the typical cheat skills of an isekai MC, it doesn't really matter.
Despite having the body is a skeleton, Arc must still be able to feel things; the bath didn't look like only a spiritual experience for him.