The only answer I can give here is one you likely already know. Upgrade your distro.
18.04 is nearing end-of-life for the main 5 year support cycle.

Kisak repo was generally okay for me when using Ubuntu 20.04+. Can't vouch for Ubuntu 18.04

As @dpanter has already said, I would strongly recommend upgrading your distro

FWIW, I'm asking this because I'm trying to find a way to get recent drivers on the older Ubuntu in our CI, upgrading which is not currently in priority.

At home I'm obviously using something much newer :)

Still looking for an answer. I wouldn't believe there's no way to upgrade graphics drivers on Ubuntu 18.04!

honestly you would be best served by updating to the newest lts and use kiosk. Or chose a
rolling release distro like opensuse tumbleweed or arch.

Still looking for an answer. I wouldn't believe there's no way to upgrade graphics drivers on Ubuntu 18.04!

Of course there's a way, we're strongly advising you to upgrade instead since there's no point in doing it for this ancient distro release. If you have a mission critical machine that can't be upgraded then leave it the hell alone, if it's not mission critical then upgrade to the most recent release you can. 22.04 LTS has been out many months now.

You have been warned... here be dragons.

You have been warned... here be dragons.

This is probably the fastest solution for such a request.

The other alternative would be to compile Mesa from source, but it can be very time consuming.