Raspberry Pi OS (32/64-bit) with desktop based on Debian Bullseye Raspbian:

wget -O - http://dicaffeine.com/repository/dicaffeine.key | sudo apt-key add -

echo "deb https://dicaffeine.com/repository/ bullseye main non-free" | sudo tee -a /etc/apt/sources.list.d/dicaffeine.list

sudo apt update

sudo apt install -y dicaffeine

If web update is not working, you can try update manually using the console commands:

sudo apt update

sudo apt upgrade -y

sudo reboot