I am not very familiar with Proxmox, but it might need some tweaks in the virtual disk configuration? In your config, the LVM Thin disk is attached as a “raw” disk to the HAOS VM?
The script shared in Installing Home Assistant OS using Proxmox 8 adds discard=on,ssd=1
to the virtual disk configuration, maybe that helps?
FWIW, HAOS runs a fstrim systemd service once a week. This should help for underlying disk systems to understand which blocks are actually free. So after enabling above options, it might take a while for virtual disk/Proxmox to learn which blocks are actually free.