To address the major concern, last chapter, the Author explicitly showed that they were in the music room where they were putting up supplies and that there was a Piano in there. This did not show up randomly or out of nowhere, it was there since the beginning.
This is also the song from the START of the Valentine's Day arc, because it's where the idea was first brought up. Being able to play piano is not THAT much of a special skill and it's not unusual to think that a high schooler would be able to do it. Additionally, MC brings up that his father was very into western music (probably what got him into the piano) and enka music (which is traditional Japanese music and has heavy use of string instruments, pianos, and vocals)
Additionally, he, himself. says the performance of the song is "unforgettable," which would make sense that he would know it and take steps to learn it after the fact because he has a crush on her.
Also, if you take the arc holistically, it makes sense it would conclude this way because it starts with the three of them bonding over mutual affection/using music to unite them and ends with all three bonding over music, with the Valentine's day chocolate being brought up midway through. It's book-ending the arc more than anything. So no, this is not just pulled out of nowhere or the author's ass, but has been built up in some meaningful way.
Just an observation I thought that y'all might enjoy to help explain it away.
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