Possibly, this is more mimicing behavior than actual creative ingenuity but….I had a damn Mockingbird that learned to mimic my phone one year. I would go running to answer it and realize it was the bird in the yard, it was uncanny how he/she sounded EXACTLY like my phone. lol
I know the pair of House Finches that nested in the corner of our big front porch here were quite creative, building their nest in a tangle of light cords that formed a little pocket at the end of the porch from where the deck lights all connect. It was the prefect cradle.

Rock-a-bye birdies. haha

I’m no avian expert, but I would think they sing reflexively rather than creatively—yet no less pleasingly to human ears.

Birdsong is creative and sounds more fresh and original than most noodling on a guitar. Let’s not forget however it is meant for other birds and perhaps God rather than us humans.

Ask the bower bird!

Less exotically, song sparrows are an interesting bunch. They have a complex song that isn’t uniform among the species but varies between individuals. I notice that for the most part their calls start and end with a series of rhythmic notes, but in the middle it’s a free for all of trills, buzzes, and other interesting sounds.

I pass lots of them on my walk to the train station and I’ve started to notice that there’s one individual who’s a little…..how should I say it…...special. Rather than the elaborate trilling and fancy cadences of his fellows, in that middle part of his call he just sticks one long, low, loud BUZZZZZ. It’s ugly as hell and I keep wondering if he’s going to get a mate or wind up lonely because of his lack of creativity. I found it so funny that I recorded it a few days ago.