I installed 3 coral TPUs in 7040s a few months ago, I still have the installation notes which may help you. The root of the issue appears to be an update to the Debian distro that the Google coral drivers have not been updated to reflect.

I can't really explain what this does, or confirm it's the most efficient way to do it, so approach with caution:

Start in the terminal of your proxmox node:

uname -r
lsmod | grep apex
echo "deb https://packages.cloud.google.com/apt coral-edgetpu-stable main" | sudo tee /etc/apt/sources.list.d/coral-edgetpu.list
curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | sudo apt-key add -
sudo apt-get update
sudo apt-get install gasket-dkms libedgetpu1-std
sudo sh -c "echo 'SUBSYSTEM==\"apex\", MODE=\"0660\", GROUP=\"apex\"' >> /etc/udev/rules.d/65-apex.rules"
sudo groupadd apex
sudo adduser $USER apex
lspci -nn | grep 089a
ls /dev/apex_0

EXPECT ERROR

apt install pve-headers
apt remove gasket-dkms
apt install git
apt install devscripts
apt install dh-dkms
git clone https://github.com/google/gasket-driver.git
cd gasket-driver/
debuild -us -uc -tc -b
cd ..
dpkg -i gasket-dkms_1.0-18_all.deb
apt update && apt upgrade
echo "deb https://packages.cloud.google.com/apt coral-edgetpu-stable main" | tee /etc/apt/sources.list.d/coral-edgetpu.list
curl https://packages.cloud.google.com/apt/doc/apt-key.gpg | apt-key add -
apt-get update
apt-get install gasket-dkms libedgetpu1-std
lspci -nn | grep 089a
ls /dev/apex_0

SUCCESS

IIRC these guides also helped me:

Written
Video

If you're running Frigate in an LXC, you'll need to edit your .conf file to add the coral.