Thinkpads have matte (upto 4k) displays, very good Linux support and are around 2000 USD/EUR.
Writing this from a X1 Gen9, I wouldn't call the following "very good". Not sure if it's already fixed in new firmware (and couldn't google the support forum right away), but I had to
* switch sleep mode to stop it from getting hot while asleep;
* disable touchpad in BIOS to stop it from spinning fans while awake — great for me because I don't like it anyway and vastly prefer the trackpoint, but people not used to this consistently go wtf while trying to show something on my laptop.
Never had the touchpad issue though.