You can install this package manually but you will have to check for updates manually here.
First, download the deb file (assuming you are using the amd64 version of Ubuntu):
Then, install the package:
sudo apt install ./libpipewire-0.2-1_0.2.7-1_amd64.deb
Since libpipewire0.3 uses a totally different set of files, there should be no conflict.
Again, you will have to manually check for updates. The current version is 0.2.7-1. When you see a newer version, just click on "amd64" under "Architecture" and then you can either click on one of the mirrors to download the file or copy the link and paste it into the terminal to use the
wget command to use the same method as above. Just make sure to use the correct filename with the
apt command so that you don't install the wrong file (like an older downloaded version).
Finally, there is some additional information on the Archlinux wiki that you may want to check out where they mention that you might have to install
xdg-desktop-portal and enable the chromium flag
chrome://flags/#enable-webrtc-pipewire-capturer to get it to work.