As a long-time Fire Emblem fan, although admittedly a mediocre player of the games, Fire Emblem: Three House is certainly a game in the series. While that sounds negative, in my experience Fire Emblem struggles to combine good gameplay with good story. 3H falls into the latter category with an engaging story that is nuanced and complex, with many different dimensions to observe it from.
The plot and characters have genuine depth that is often neglected in Fire Emblem games, bringing the best written characters in the series. The plot itself struggles to fully develop the themes of the games and reeks of being rushed and unfinished, especially due to the two of the storyline paths being nearly identical and another being shorter than the other ones. Not to mention Those Who Slither and Add Little to the Plot.
Gameplay is... fine. It functions, it is fun, just not particularly deep. Much of the gameplay is routing enemies with not too much diversion from that. When it does divert from that, the game improves, with more intensive and memorable moments.
While the characters are fun to customize, it does lead them to lose a sense of identity, which somewhat goes against the Fire Emblem character formula. The individual personality and backstory will keep you engaged with them, however.
In conclusion, Fire Emblem: Three Houses is a good direction for Fire Emblem with complex plots, themes, characters, and customization, but doesn't quite stick the landing in many ways, with a seemingly rushed execution and gameplay that can come off mindless due to its lack of variety.