The short answer
Yes — soft, sweet banana is a safe and easy budgie treat.
Why
Banana is gentle on a budgie's digestion and provides potassium and vitamin B6. Its downside is sugar, so it belongs in the treat category rather than the daily veg bowl.
How to feed it
Peel it and offer a thin slice or a small mashed amount. Banana browns and spoils quickly, so remove any uneaten piece after a couple of hours.
How much & how often
A slice 2–3 times a week is plenty.