I've got a Framework Laptop 13, 12th gen Intel (Core i5-1240P). I am running Fedora Workstation on it with no issues. I think I had to do something to get the fingerprint reader to work, but it wasn't a big deal from memory.
- Linux: It works and they support 2 distros officially.
- CPU and RAM: There are 3 different CPUs to choose from at various prices, and RAM can be specced up to 64GB (or BYO RAM).
- Lightweight: 13" available (and a new big daddy 16" with dedicated GPU selling now).
- Touchscreen: Sadly, no to this one.
- USB-C: It's all USB-C, and they have this cute gimmick where you can turn the USB-C ports into anything with expansion cards; USB-A, HDMI, Ethernet, etc.
- Battery Life: Can't comment on this, as I always have mine plugged in. But I have seen reviews and videos saying around 6 hours is the average life time from a full charge.
Here's a Framework post clarifying what they support verses what is compatible. Also has links for Ubuntu 22.04 installs and Fedora 39 installs.
There is Tuxedo Computers, who are based in Germany (so prices are in euros). They develop their own Linux distribution, Tuxedo OS which is KDE based. All hardware is either selected or purpose built to work with Linux. I have never used or purchased their laptops or desktops, as I don't think they ship to Australia. If you wanted to try them, you would have to go with mail forwarding service, if that is even a thing. I usually watch The Linux Experiment reviews when I am feeling noisy. Just a caveat, I think he sometimes gets sponsored by Tuxedo.
There is also System76, which is in the USA. I personally wouldn't bother, as the shipping prices to Australia were ridiculous when I was looking at buying a Launch keyboard from them. They develop their own distro too, if that sways you.
There is also the usual suspects like Thinkpads or Dell XPS like you have ๐