I apologize for being brash, but I believe that you kinda missed the mark.
Supergirl has ONE very short scene, and in that moment she's putting on a front of being carefree and rebellious, masking her true feelings... An attitude which Superman himself doesn't fully approve in the scene.
Why would they give away and spoil Supergirl's character (development), when that's her starting point in the upcoming movie?
Also, the scene is not really a sequel tease, it's more of an easter egg which sets up the fact that Supergirl exists in this universe, her relationship to Superman and Krypto, and status quo / current mindset.
As for James Gunn on Superman, I don't think that he robs dramatic or darker moments through jokes. There's a nice balance and tonal switches to make sure that the different tones have the right amount of space to breathe and truly settle in. He also doesn't shy away from uglier moments in the story.
I find his movies (and series) to be emotional rollercoasters, where you laugh one moment, and try to hold back tears the next.
But hey, opinions.