Hi matetwo,
I completely understand:
UNetbootin is not found as an install possibility.
Let's find out why
This is the homepage of UNetbootin:
https://unetbootin.github.io/linux_download.html
quote:
To install UNetbootin from the Ubuntu PPA, run the commands
etc etc.
So UNetbootin is not in de regular repositories.
The embedded link on that page, links to an Ubuntu PPA, this PPA:
But there are no versions for Jammy
Workaround:
You can download the previous version by clicking this link:
https://launchpad.net/~gezakovacs/+archive/ubuntu/ppa/+files/unetbootin_700-1~groovy1_amd64.deb
And then doubleclick on the downloaded packet. This should install UNetbootin.
After that, issue this command:
sudo apt install extlinux
Otherwise UNetbootin starts complaining that it needs 'extlinux'
I just installed it and I'm running UNetbookin now (while writing this).
It is at the moment writing the ISO of the previous UM version to USB-stick.
So far so good ... 
EDIT: The above mentioned session produced a perfect ubuntu-mate bootstick 