So... is Bishounen Tanteidan finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: June 27, 2021
Manga finished: May 14, 2021
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Mayumi Doujima, haunted by the memory of a specific star she saw in her childhood, seeks to find it before her fourteenth birthday deadline. She fears losing her dream if she fails.
Enter the Pretty Boy Detective Club of Yubiwa Academy, a group of strikingly handsome young men who abide by very specific rules. They offer their unique services to help Mayumi in her quest.
Mayumi possesses an extraordinary gift: exceptional eyesight that allows her to perceive details invisible to others. This ability, combined with the Pretty Boy Detective Club's skills, might be key to finding the star.
However, the search for the star unexpectedly leads them into a more complex and potentially dangerous mystery, hinting at a deeper story than a simple childhood longing.