In the very beginning of the chapter, it is the first new morning that Illya and him have seen for (more than) a (subjective) month. Even more importantly this is the first time Illya sees the loop finally breaking, it's the first new morning she's witnessing since waking up from the night she fell for the MC. Far from a heavy atmosphere, they (and especially Illya) should be overjoyed. And she should be very relieved that MC's (seemingly insane) rambling about having sex with star women, actually, somehow, really did manage to break the loop. (Reminder that
she could never even see the star on the nun)
And not immediately telling the truth to the nun is kinda stupid. Sure, extrapolating from a sample size of 1 is a dangerous wager, but if we go by Illya's experience they could predict that :
- There will be more looping days. (which is likely to be the very day they're currently in)
- The nun is now part of their group and will (just like them) remember the events of the past versions of the same repeating day.
As such, considering the nun's faith, character, and opinion of them, they're bound to face a serious conflict when the nun realises she's trapped in groundhog day hell, and the person she reveres as a god :
a) is powerless to stop it
b) was probably the reason she got trapped in the time loop
c) seemingly tried to keep exploiting her faith in him until pretending became untenable
Immediately coming clean to her about the situation is probably the safest path to proper collaboration. Well, would be if MC didn't have the power of hentai protagonist and plot armour with him; and all lies and abuse will be forgiven, forgotten, or straight up ignored under the rock solid justification that she loves
his dick him.