In the same way that earlier vocal distortion represented God, the effect on his voice in "All Eyes on Me" seems to signal some omniscient force outside of Burnham.
In this case, it's likely some combination of depression/anxiety/any other mental disorder.
The song's melody is oddly soothing, and the lyrics are a sly manifestation of the way depression convinces you to stay in its abyss ("It's almost over, it's just begun. Don't overthink this, look in my eye — don't be scared, don't be shy, come on in the water's fine.")
Depression acts like an outside force, one that is rather adept at convincing our minds to simply stay in bed, to not care, and to not try anymore.
The song brings with it an existential dread, but Burnham's depression-voice tells us not to worry and sink into nihilism.
"You say the ocean's rising, like I give a s---," he sings. "You say the whole world's ending, honey it already did, you're not gonna slow it, heaven knows you tried. Got it? Good. Now get inside."
The whole song sounds like you're having a religious experience with your own mental disorder, especially when new harmonies kick in. It's a dangerously tempting invitation to stop caring, coming from the villain of this musical comedy (depression).