Fire Emblem: Three Houses was the first home-console Fire Emblem since Fire Emblem: Radiant Dawn.
Radiant Dawn launched for the Wii in 2007 and continued the story of Path of Radiance, the 2005 GameCube entry. After that, the series focused mainly on handheld systems, including the Nintendo DS and Nintendo 3DS.
Three Houses returned the main series to home consoles in 2019, releasing for the Nintendo Switch. Its development followed the commercial success of Fire Emblem Awakening, which helped restore confidence in the franchise after weaker sales. Intelligent Systems also worked with Koei Tecmo to expand the project for high-definition hardware.
A common mix-up is Path of Radiance: it was the previous home-console game, but it was not the most recent one before Three Houses. Radiant Dawn came after it and was the Wii title referenced by the question. Three Houses also introduced a notably different structure, combining tactical battles with teaching, calendar management, and social interactions at Garreg Mach Monastery.