No date announced yet. The new PV is here. This announcement comes as the season 2 finale aired today. Check out the ANN article for additional information. Synopsis of the first season from AniList:
When a pregnant young starlet appears in Gorou Amemiya’s countryside medical clinic, the doctor takes it upon himself to safely (and secretly) deliver Ai Hoshino’s child so she can make a scandal-free return to the stage. But no good deed goes unpunished, and on the eve of her delivery, he finds himself slain at the hands of Ai’s deluded stalker — and subsequently reborn as Ai’s child, Aquamarine Hoshino! The glitz and glamor of showbiz hide the dark underbelly of the entertainment industry, threatening to dull the shine of his favorite star. Can he help his new mother rise to the top of the charts? And what will he do when unthinkable disaster strikes?
I think you are probably referring to Chapter 122 (or thereabouts). I think a season 3 could reach that far. After two seasons we ended around chapter 80. It was helped along a bit by a triple-length episode one though. I am not quite sure where season three will end, but so far this adaptation has been excellent and I fully trust them to pick a great spot.
Specifically
spoiler
the end of Chapter 123