My impression was that only a few niche applications have bothered (notably, Photoshop has had support for a few years), since 10-bit displays are so rare/expensive, but I’m not an expert.
As for Linux, as far as I know the stable version of GIMP still only supports 8 bits/channel color, so displaying at higher bit depth is right out. I guess maybe some specialized video or 3d rendering software could use a 10-bit display? I doubt typical Linux apps support it.
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Edit: In doing some web sleuthing, there seem to be endless issues with compatibility. (As you’d expect from a new technology that requires upgrading every part of the pipeline for support: applications, operating system, video card drivers, video cards, display interface, and the displays themselves)
I see this on a random web forum: “I got an answer from an engineer at Adobe, why Photoshop CC cannot display 10bit/color under Windows 8, 8.1 and 10: There is no OpenGL-path with 10bit/channel like in Windows 7 any more :(”
Adobe’s troubleshooting site says “Note: 30-bit display is not functioning correctly with current drivers. We are working to address this issue as soon as possible”