How I see it is that the author didn't delve into the physics of the reincarnation bc this type of story (romance?/psychological drama) wouldn't benefit from overly explaining how they came back to life, bc they prioritise the emotional journey instead. So you could say the tragic ending of their first life is simply the narrative motivation for the regression, like there had to be a do-over yk?
And if sejin remembered everything in their second life, the story would make no sense. He would simply reject the marriage proposal and even run away bc why would he marry the man who drove him to his death? And it also wouldn't serve the purpose of ido's penance in the second life as he works on undoing his past mistakes while caring for and protecting sejin.

Wait so I’m confused how exactly did they get a second chance? How was it possible for them to get a second chance to redo things? And why only did the ML remember everything