[Verse 1]
Did you notice, babe
Everything is alright?
[Chorus]
You need me
Rest easy
[Verse 2]
Maybe leave something secret behind
Never thought I'd sing outside
[Chorus]
You need me
Rest easy
I'm here
How weird
Mike (Perfume Genius) has stated many times that due to his prior drug addictions he has had problems getting in a relationship, Alan was his first actual relationship, here he is stating how weird it is for him to actually have something (a relationship) after so much struggle.
Mike is talking about how he and Alan sleep peacefully through the nights without any trouble or nightmares since they are together.
Could possibly also be a hint to (a light form of) insomnia which is mostly or entirely gone now.
Mike was expecting himself to not go full into this relationship by not telling the truth all the time (hiding behind his lies) and therefore play a self-destructive role in this new relationship. Instead of these expectations, he got the complete opposite: he found someone he feels completely comfortable, appreciated and loved with. Someone who listens and understands everything Mike has to tell to him. It got Mike the happiness he was looking for, making him sing outside (probably on the street, not giving a fuck what other people think).