Just get a Thinkpad. They have all the features you want. They're not going to be as thing and light, but their keyboards are better than anything out there. The touchpad is iffy, but if you're using Linux (I use it too), your touchpad experience is going to be subpar anyway.
I have an X1 Yoga which is capable of all of these things. It is a laptop with a good keyboard setup that can hold up it's own screen w/out a kickstand. When I don't want the keyboard I just fold it up and the keyboard changes to lift and lock so the back of it is solid making it easier to put on a stand (or A frame it and use a couple of books in a pinch. They sell one with linux preinstalled too.
This is especially a problem on the older models. Some Thinkpads are really excellent machines besides their unfortunate 720p, TN panels.
Admittedly though, Lenovo seemed to get their act together on later laptops. My T460s has a matte 1080p display with 90%+ DCI P3 coverage, which is pretty good for a $300 used laptop.
I ordered a 1080p screen and controller from Aliexpress for my trusty old Lenovo T420. Installed in about 30 minutes and worked perfectly. The difference in image quality versus the original crap panel is huge.
Older Asus fold had many issues with Linux. In most cases, you can get headless mode working but forget about GUI. A better solution would be trying out System76, HPDevOne or Dell XPS dev edition for Linux desktop.
The Purism Librem 14 isn't half bad either. Currently using it. Love the build quality of the case, matte screen and kill switches. Quality of the built-in speakers is not that great. Keyboard is acceptable. The trackpad is nice and big.
Most likely only if packaged in ChromeOS or Android workloads, which isn't what you're asking for, but is what OEMs care about after the netbooks market vanished.
I have a Surface Pro 7 and it's great for this. It doesn't have a matte screen but does the rest of it well. I'm running PopOS on it and switch between the included keyboard and an external keyboard with it on a tablet arm.
Should be back in stock "soon"... Though I'm keeping an eye on the pipenote instead now - more powerful CPU. Instead of LCD it is epaper which as pros and cons for this use.
A tablet with a matte screen.
That can run Linux.
So I can put it on a stand and a keyboard in front of it.
That would be the ultimate travel setup! Working in cafes without having to look down all the time.
Does something like this exist?