This is obviously a follow-up to another thread, but I decided to create a separate thread as those issues have been resolved and everything is working perfectly (many thanks for bringing them to your attention!)
The problem now is that the texture is clearly being saved in a linear colour space.
Yes, exactly. Thank you very much.
To save in the correct format, you need to specify the correct format when rendering.
I specified R8G8B8A8_UNorm_SRgb and everything started saving as it should.