Outside of mating season, birds definitely do sing just for fun.

And even in mating season, I wonder if birds really consciously try to "get laid" or if they just sing, because it feels like the right thing to do in the moment and then getting laid happens. I mean, some start singing very young. How would they know what it's for the first time? Not all birds are as smart as crows.

This review paper looks at the motivation for both kinds of singing: intrinsically motivated (just for fun, all year round) and singing that attracts mates. In the latter, it's unclear, what triggers the motivation. The author supposes, it might be a combination of socially reinforced behavior and the vicinity of a mate, rather then the act of copulation, that triggers the reward.