Might as well.
I think this is closer to the truth. There are overarching themes across the games, of course, but individual games can also have their individual "messages". Some of these messages you might have to squint at to see, because I don't think ZUN overall tries to deliberately insert a specific message very often. But they do happen.
Would be a fun topic to explore in its own thread, too, I think.
Honestly, I really don't go into the story of Touhou games, other than the general gist of them.
So, a possible TL;DR of all the games so far: Invasions from two alternate dimensions, invasions from alternate dimension (with a ghost!), mysterious ruin, invasion from an alternate dimension, invasion from an alternate dimension (now with devils!), a vampire that makes red fog to go outside, ghost is curious about a cherry tree, loli oni wants a party, lunatic Lunarian lunacy, too many flowers, crow takes pictures, new gods of the mountain, celestial is bored, geyser because of god-eating raven, interdimensional flying ship because geyser, a dream/ice fairy adventure/fighting your ancestor, two crows take pictures, more adventures with ice fairy, resurrections because of interdimensional flying ship, religious wars, contrarian and midget vs. everyone, just contrarian vs. everyone, occult stuff, and more lunatic Lunarian lunacy (now with invasions!).
So have fun!