It is definitively impossible to define a song, its lyrics, or the vocal performance behind it, "overdramatic" without knowing what inspired it or what personal meaning it holds with its creator. You're making snap judgments because you don't like this band or their (heavily) earnest songwriting, but that doesn't mean AJ is being histrionic.
I don't dislike this band, I've just been greatly disappointed in them in the past so I've been very weary of them. and you're right, I don't know what the personal meaning behind it is, but this song makes me not want to care at all. the band has been singing all too similar tunes for a while now and it's getting very tiring.
look at eminem, sure his new albums are meaningful to him and I don't know what they're all about because to me, eminem's music hasn't progressed in any way and/or lacks anything interesting (i.e. he's a one-trick pony that refuses to learn new tricks that are anything worthwhile). same thing with this band, I really can't care about the meaningfulness of their new songs like I did with northern lights or permanent rain because they don't sound like they're going anywhere with their music. and I don't care how meaningful this song is because I don't care about the song itself - the instruments, the aesthetic, the histrionic singing that sounds forced.
I'll use anberlin's *fin as an example, sure the song is incredibly significant to the band/singer, detailing the singer's personal experience and struggle with religious convictions, etc. and now say that I didn't care for the song at all (which I do, just using this as an example), are you going to expect me to care about any of that? you shouldn't. and you should definitely expect me to think he's being overdramatic in his impromptu outro.