Not licensed in English. Complete at 3 volumes. Apparently this series was axed so the ending is rushed, but a sequel was approved and apparently has a proper ending (the title is similar but has "Reload" in it, according to the comments).
Series info:
https://www.mangaupdates.com/series/x7y9otd/i-took-a-trip-to-an-otome-game
1/25/24(? That's what my browsing history says but it feels like longer ago) (V1E4)
I ♂ Took A Trip to an Otome Game