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Exported FBX file has incorrect albedo colors (linear/gamma issue)
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Description

System Information
Operating system: Windows-10-10.0.19041-SP0 64 Bits
Graphics card: NVIDIA GeForce RTX 2070 with Max-Q Design/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 472.47

Blender Version
Broken: version: 2.93.6, branch: master, commit date: 2021-11-16 14:54, hash: rBc842a90e2fa1
Worked: none? not sure

Short description of error
Exporting the attached blend file to FBX results in an incorrect albedo color (too dark) in the resulting file.
The result file can be viewed in e.g. Unity or Windows 3D VIewer


In Blender


In Windows 3D Viewer (the incorrect triangulation is a Windows 3D Viewer bug)

Exact steps for others to reproduce the error
Download


Note light green color
Export to FBX
View in Windows 3D Viewer or Unity or ...
Note incorrect dark green color

Create a new scene in Blender and import the file
Note incorrect dark green color (so import seems to still interpret correctly)

Event Timeline

Your assessment is correct about gamma. However, FBX files do not specify any color space information and the specification doesn't enforce one, so this is left up to the software.
The FBX exporter exports the color directly as [ 0.237069, 0.401970, 0.114849], which is the correct linear color in Blender. An option to control this could be added, but this is considered a TODO and not a bug at the moment.
See Bastien's comment here https://developer.blender.org/T53209#468514.