I have a clue of what might be the cause of the difference in exposure and color rendering, but before I present the clues, let me post a big of disclaimer. I don’t have PureRAW 3 installed. I use DXO PhotoLab so I don’t have the need for PureRAW, because PhotoLab offers everything Pure RAW does plus a lot more.
That being said, upon downloading the files you provided and opening them in PhotoLab, I see that they is difference in exposure and color rendering, but difference seems to be probably result of color profile mismatch. Let me share what I found.
This is the two files. Original RAW from Fuji XT-4 (on the left) and Linear DNG processed in PureRAW on the right.
This is how original raw looks like in PhotoLab. If you look at the color rendering you will notice that the file has film simulation color profile applied. The Fuji Classic Chrome. I imagine this was added in camera.
And this is how the linear DNG processed in PureRAW looks with the embedded color profile. Its more saturated and a bit brighter.
However. As soon as I switched to Fuji Classic Chrome profile in PhotoLab, the colors and exposure match the original raw file very closely. With vignette correction in the DNG. so its brighter because of that.
My theory is that Fuji camera records film simulation color profile in the RAW file as it comes out of camera. In this case its classic chrome, profile. When you process it in DXO Pure RAW , I am not sure if that is honored of the profile reverts back to just standard color rendering for Fuji XT-4.
If you use PhotoLab instead of PureRAW you can manually choose color profile that matches the film simulation of the Fuji camera. I think that could explain the difference in appearance.
Try to shoot another image with your Fuji XT-4, choose a standard Fuji profile for XT-4 and not the film simulation and than try to process it in DXO PureRAW and see if the color and everything matches. If so, than the problem is in the fact that probably PireRAW, unlike PhotoLab, does not support custom film simulation profiles that Fuji camera can use. You can still get the look you want, but you would have to apply a Fuji color profile after you have saved it as DNG.
Hope that helps.