There does not appear to be an authoritative answer on availability of rpi-eeprom-update for Ubuntu 20.04.
Please take note of James Chambers's comment from his GitHub:
Ahh yes the new bootloader firmware utility.
This utility is only available on Raspbian at the moment. I think mostly nobody dares to risk bricking everyone's Pis because if you look at the source code at GitHub - raspberrypi/rpi-eeprom: Installation scripts and binaries for the Raspberry Pi 4 and Raspberry Pi 5 bootloader EEPROMs it makes extensive use of the /opt/vc tools (some of which are not open source). The 64 bit build of these tools is known to be partially incomplete and poorly tested. I build the absolute latest vc tools in this image but I wouldn't trust them to perform this update correctly.
Right now no distro has dared to include this utility and I definitely wouldn't be the first because I would never put all of your Pis at risk like that. If something goes wrong when using this utility you can brick the Pi.
I have written extensively about this utility here: Raspberry Pi 4/400 EEPROM Firmware Update/Recovery Guide
The most important thing to understand is that the rpi-eeprom bootloader updates are permanent. Reformatting your SD card won't affect them as they are actually flashed onto a special EEPROM chip inside the Pi. This means that if you have a spare SD card or just install Raspbian and then install the bootloader updates you can install anything you want after that.
I actually keep a spare SD card with Raspbian on it just to safely flash these updates.