The formula you're describing is actually more extensive - and also less original - than you suggest.
It's not just "love songs" and "showstoppers." Though those are often central to those movies, I would argue that the "I want" songs (Part of Your World, Go the Distance, Reflection, Out There, etc.) are often the anchoring cores of those films, and often the most iconic and emotionally resonant. But in addition to those, you also often have the "villain song" (also, more generally speaking, the Disney Villain archetype also had its Renaissance during that period, and they're considered something a dying breed - replaced with "twist villains," or no villains at all).
But these iconic song formulas ("I want" songs, love songs, showstoppers, villain songs, etc.) aren't something that was invented by Disney. The reason the Disney Renaissance happened in the first place was largely because of their employment of classic principles of musical theatre. Before the Disney Renaissance, Disney had plenty of animated movie-musicals, but the song-placements tended to be less thought-out, and the songs themselves weren't rooted very deeply in nuanced storytelling. They were just often just hummable anthems sung by a chorus, or fun ditties to liven up the comedic scenes. And the few character-driven songs tended to be very generic in terms of their content.
It was really the late, great Howard Ashman who stepped in (at one of the lower points in Disney's animation studio), and became a driving artistic force behind these movies, and it was largely his doing that the films became rooted in the principles of musical theatre, which prioritized storytelling through music more than anything else. The recent documentary about Ashman explores this very effectively.
And after Ashman died, his successors (especially Alan Menken) carried on that legacy through the end of the Disney Renaissance (though you could argue that Tarzan breaks the mold - and Tarzan, perhaps not coincidentally, is widely regarded as the final film in that era).