What do you think?
Should activities like bird singing competitions be considered gambling or just a normal contest with prizes?
It has all the elements that make it gambling-based, based on the parameters you've sent, but if the organisers did not encourage side bets, then it can be considered a contest. If there is no ticket or betting booth where you can bet on which bird will win, then it's a contest.
You did mentioned
Sometimes people make side bets on which bird will win
So it's a bet between people and not encouraged or sponsored by organisers, so this Bird singing is a contest because the organisers did not encourage betting.