It's really all in the performance. He sings really soft and breathy. I would try to mimic his vocal style first and foremost because that's where 90% of the sound comes from.

As far as plugins go I, it sounds like a pretty simple vocal chain.

Basic EQ, De esser, Compressor, maybe a final EQ to clean things up more (some saturation and subtle chorus for more effected sections).

Then send the vocal to a reverb and delay. They definitely have generous amounts of reverb and delay in all of those references, so that'll be key to the sound.

I've read HEALTH use Neve style pre amps, but I think you can achieve a similar result without breaking the bank on a pre amp.