I feel like reincarnators put too much importance on keeping their other life a secret. especially when it's to someone they love. I mean they loved you and only know YOU. they never knew the person that was you so is that even important. besides maybe getting surprised it would be like finding out they are from a different country than you originally thought.
well Fl is a bit different cuz she actually got traumatized by her death but that's not the reason why she didn't tell Izu