Laptop/win10/Edge 90.something. Starts (drum roll) after 1st gate with zero souls. (!!) Didn't expect that. Must be storing part of it on the server side, or in "the cloud", based on [IP address] or - dunno clueless.
I was gonna say "might want to consider a reset-game option at some point". From my pov this little experiment bumps the priority up a little bit.
Dunno how you puzzled out hwcdn. Edge does show 67 bytes stored there, while Firefox didn't show it at all. I'll try deleting that after I post this.