How do I cope as a supervisor carrying everyone's trauma with no one supporting me?

You hold your supervisees, and through them you hold their hardest cases too. All that weight lands on you, and no one is holding you. That is not sustainable, and it is not a personal failing to feel it crushing. It is too much for one person to carry alone. The truth you teach others applies to you: no one heals while holding it all in silence. You need your own support as much as any client does. This is not a luxury. It is the thing that keeps you able to do the work at all. Find your own holding this month. A supervisor for yourself, a consult group, a therapist. Say the hard cases out loud to someone whose job is to catch you. You cannot pour from a cup no one ever fills.