So I have spent my last 4 days to try get proxmox working with an nginx proxy. Due to how proxmox is built up I had to get clever with some rewrite, break some nginx rules and spend sleepless nights awake to try figure this out (to be honest I am no genius on web servers as I rarely have to touch them). Plus it seems like nobody (from my googling) had managed to set proxmox up to work behind a proxied subdir, understandably so as some of the html generated uses absolute paths for sources instead of relative paths and you need to deal with that.
This is the proxmox.conf file i ended up making (Replace all instances of pve.local:8006 with your internal proxmox ip and port) And replace publicwebsite.com with your website domain
NOTE: THIS IS FOR PVE6 and I have no plans to fix for PVE7 as I do not need it behind a reverse proxy anymore.