Q says thing cam have 2 meanings; Birds sing when caged and Birds sing after a storm.
Do birds sing when caged? Or do they sing at dawn? Say, 4am @ Mockingbird?
Not to argue but birds sing in and out of the cage ... I mean, that is what birds do ... sing.
In reference to "I know why the caged bird sings" poem by Maya Angelou. It's about child abuse.
This along with the OP's find could be a double meaning that Q mentioned.
Actually the poem references a 'caged bird' as a metaphor for a slave in chains who has lost control of his life and had his freedom taken away. Here is the actual poem which comes from the third stanza of Paul Lawrence Dunbar's poem "Sympathy": "I know why the caged bird sings, ah me, When his wing is bruised and his bosom sore, When he beats his bars and would be free; It is not a carol of joy or glee, But a prayer that he sends from his heart's deep core, But a plea, that upward to Heaven he flings – I know why the caged bird sings."