Most JPEG XR files I’ve seen are linearly encoded with sRGB gamut (Microsoft calls it scRGB - more detail on why in the next paragraph). Many viewers might assume that and behave badly if presented anything else. Note that if a viewer assumes linear data and you feed it something that is gamma or log-encoded it will appear EXTREMELY washed out - kind of the opposite of what happens when you misinterpret linear data as being gamma or log-encoded (extremely dark)
Before you say that sRGB gamut is too narrow - since JPEG XR encodes floating point values, it can encode out-of-gamut colors using negative values for R, G, or B. This is why MS calls it scRGB ( scRGB - Wikipedia ) - although in JXR, usage of float32 eliminates even the scRGB limitations discussed in that article - no practical limits on magnitude of negative or positive values.
JXR is used extremely rarely around here - the limit of my experience/knowledge with JXR is from JPEG XR (*.jxr) file format support · Issue #6612 · Beep6581/RawTherapee · GitHub and Python image conversion scripts - intended primarily for RawTherapee input but useful otherwise
Wrong, see above regarding scRGB with float representation
EXR is the same - nearly every EXR example I’ve found is linearly encoded using sRGB primaries, which again is NOT a gamut limitation in any float-based format that can encode negative values for color components.
Rec.2020 gamut + PQ or HLG transfer function is almost never used with float encoding, because the whole point of those is to work well with formats that rely on unsigned integers to represent everything (typically 10-bit unsigned integers). I would not be surprised if many JXR viewers assume sRGB primaries and linear encoding regardless of metadata, just like many JPEG viewers without proper color management assume sRGB primaries and sRGB transfer function.
JXR was designed to be easily viewable on sRGB displays - clamp all floats to [0,1], apply sRGB transfer function to the result, done. Yeah you clip highlights and clip gamut instead of a more appropriate tonemapping, but 95%+ of the population won’t notice. Especially since a lot of game developers tend to minimize their gamut/luminance excursions outside of the sRGB space since there’s such wide variety of HDR display capabilities right now.