Never been in your position but DS2 gets bouts of mild depression (ie no rason for them, low mood lasting for days or weeks.) It is very draining. But as I also suffer long term depression (which I manage very closely all the time so it doesn't impact on DC or family life) I have a lot of sympathy, and some practical tips.
I focus on very practical things, as I do for myself when I'm depressed. Make sure he has a daily shower - gentle but firm: 'I know you don't feel like it. You don't have to want one to have one. And you will feel and smell better afterwards.'
Make sure he has daily fresh air. Again gentle but firm. We're heading out to the shops/for a walk now, get your shoes on.' If he really can't (and depression does absolutely drain your energy like a vampire) then I set up a chair or blanket and cushions out doors and bundle him out there.
Monitor his media intake as much as possible. Aim for comedies not dark dramas, upbeat music not death metal and try to scale back too much gaming time.
If he will let you, sign him up for IESO online counselling or CBT self help MoodGym programme. They are better than talking therapy if you are introverted. They feel far less like stripping naked in front of a stranger.
Keep conversations about him and his mood to limits you can handle. When time's up, end the conversation with a big kiss, tell him I love him but need to focus on DS1/DH too as I love them too and they need attention as well.
Take other DC out on one-to-one day trips so you can really focus on them.