Is it still possible to install Chromium as a deb-package on 20.04 LTS using some third-party repository?

If you are concerned about security, the most proper way to get updated Chromium without untested third party patches and without snap in Ubuntu 20.04 is to use official builds from 18.04, which will be supported until 2023.

For proper installation and future updates follow the steps.

Enable bionic-updates repo:

cat <<EOF | sudo tee /etc/apt/sources.list.d/bionic-updates.list
# for deb-based chromium. Supported only 'til 2023
# see also /etc/apt/preferences.d/chromium-deb-bionic-updates
deb http://archive.ubuntu.com/ubuntu/ bionic-updates universe
EOF

Pin Chromium packages from this repo:

cat <<EOF | sudo tee /etc/apt/preferences.d/chromium-deb-bionic-updates
Package: chromium-browser chromium-browser-l10n chromium-codecs-ffmpeg-extra chromium-codecs-ffmpeg 
Pin: release a=bionic-updates
Pin-Priority: 900
EOF

And install packages:

sudo apt update
sudo apt install chromium-browser

Et voilà! Trusted and automatically updated environment without snap bastards.

It is possible by using a third-party repository (PPA) from LaunchPad, named Chromium Beta branch.

To install, one needs to add this repository to the system by:

sudo add-apt-repository ppa:saiarcot895/chromium-beta

Then remove the snapped Chromium by:

snap remove chromium

and install the package with:

sudo apt-get install chromium-browser

To avoid the installation of the snap package in the future, one should do the following:

cat <<EOF | sudo tee /etc/apt/preferences.d/pin-chromium-deb
Package: *
Pin: release o=LP-PPA-saiarcot895-chromium-beta
Pin-Priority: 1337
EOF

To revert to the snap version, use:

sudo rm /etc/apt/preferences.d/pin-chromium-deb; sudo apt-get autopurge chromium-browser; snap install chromium