I'm seeing an issue where the values being exported, a full range of 0-1 black to white, do not match the exported map, which either seems to have the gamma adjusted somehow, or values clamp or leveled up somehow, etc. This is repeatable, other relevant info and listed below...
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What you see is the height map being normalized in the 0-255 (or 0-1) range.
The Height channel in your project is a floating point HDR channel that can display and store values below 0 and superior to 1. To keep that format, you would need to export in an HDR capable format like EXR.