So... is Meiji Tokyo Renka finished or not?
YES, it is finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Mei Ayazuki, a regular high school girl, finds herself magically transported to the Meiji era during a red moon.
She discovers a version of Tokyo where supernatural elements and ghosts are commonplace.
Welcomed by a group of historical figures at the Rokumeikan, Mei learns she possesses a rare ability to see spirits, making her a "Tamayori".
As Mei interacts with these men and navigates the unfamiliar Meiji era, her relationships with them evolve, and romantic feelings begin to blossom.
The anime explores Mei's journey as she grapples with the possibility of returning to her own time while navigating budding romances and the mysteries of her newfound abilities.