It seems to me that, following your link, 7.0.10 will end up in Noble (Ubuntu 24.04), so I could probably wait 3 month for that, but wait! Isn't the 8.x.x series expected end of January?
There are ways. You can do any of:
1) add the Noble repositories in /etc/apt/sources.list[.d], then install kicad 7.0.10 and let it pull the dependencies it needs -- but this will update parts of your system with packages from what will become Noble; it usually works fine for advanced users; YMMV, this assumes more than basic knowledge of dpkg, apt, and the principles of debian package management in general.
2) pull the deb source package for 7.0.10 from Noble (for which you need to add the respective deb-src, and only deb-src, to your sources.list) and build your own deb package that will have your current distro's library versions as dependencies -- this is the safest and usually the easiest way, when installing existing binary packages fails for whatever reason
3) same as 2, but add KiCad external repositories and pull the source packages from there, for whatever version you need. If you go this far, then there's no reason not to try 8.0, since it's pretty close to be released and is very usable as it is now. Once released, you can easily update the package (which may or may not need to be built from source on your system).
Whatever you do, before installing any new package, use
dpkg -l|grep kicad and
dpkg-repack to save a copy of what kicad-related packages are currently installed so that you can reinstall them if things go wrong. Also make sure you back up your ~/.config/kicad and ~/.local/share/kicad before running an updated version.
p.s. note that option 3 is distro-agnostic: it will (usually) work for any Debian derivative.
p.p.s. that mint-related error looks weird, as though you were on Mint at some point and then switched to Ubuntu, or installed some Mint packages manually etc. -- is the error the same for any PPA that you're trying to add, and not just kicad's?
You may grep for
/usr/lib/linuxmint/mintSources/mintSources.py in /usr/bin and /usr/lib to find out where it's coming from and/or
sudo apt reinstall software-properties-common (which contains apt-add-repository) for an easy attempt to fix it. Also
dpkg -l|grep mint,
grep -r mint /etc/apt.