Here are some stats from last night showing the volume of messages:

   IPs: 9756
   Clients: 9980
   - Google Play: 2796
   - F-Droid: 5985
   - iOS: 794
   - curl: 62
   - other: 343
   Messages: 
   - Successful: 310076
   - Failed (rate limited): 104741
   - Failed (other): 6511

   Top publishers (* = limit exemption):
   22908 matrix.org*
   22352 matrix.gateway.unifiedpush.org*
   18286 up.schildi.chat*
   16134 192.124.x.x
   14056 matrix.envs.net*
   13376 108.35.x.x
   7794 114.132.x.x
   6035 112.78.x.x
   5432 88.99.x.x
   5366 138.201.x.x   

In terms of open connections, it varies, but right now it's 5k active connections. But there are many many self-hosters out there, and the people using Firebase (no "instant delivery") are also not counted in that.

You can subscribe to the stats above using the https://ntfy.sh/stats topic (old messages are only cached for 12h, so half the day it shows up as empty)