Ok, but can’t help you with the Mac version, as I’m not in depth familiar with.
In Windows we have different viewers, which need to be properly set up.
So then for others … what viewer have you been using?
side note
Your original screenshot was not taken at min 75%, which in PL is necessary to see the colours exactly (also no chromatic aberrations).
Exporting as JPEG at a different size plus sharpening in your case with bicubic sharper can make a really visible difference.
Colour output depends on everything that is between the raw and its output. Next to the raw image file, the .dop sidecar might reveal a thing or two.
Today, I’m using PL7 on my Win 10 Desktop PC that has a monitor capable of displaying the Adobe RGB colour space. In that environment:
The Adobe RGB version opened as expected and looks the same in Affinity as it does in PL7. This is to be expected, everything is being correctly colour managed.
When Affinity opened the sRGB version it reported that it had “assigned the working profile, Adobe RGB to this unprofiled document”. This version does not look right, the colours are over saturated compared to the Adobe RGB version. This is expected because, as I noted previously, PL does not embedded an sRGB profile in the file when sRGB is chosen as the icc profile. Consequently Affinity Photo doesn’t know the data is sRGB and so it reports that the file is unprofiled and assigns its working profile (Adobe RGB) to the data. In other words sRGB data is being interpreted as Adobe RGB data and, unsurprisingly, the colours are wrong.
Been using the Mac default, Preview, but I do note the jpeg never looked right in PL7 either.
Changing bicubic sharpener to bicubic has really helped. But the sharpness of the image suffers
I exported the NEF in three ways.
With the softproofing profile, sRGB profile and Nikons sRGB profile.
I then compared them in Apples Preview.app against the preview in PL7.
There are no difference at all.
My monitor is an 27" Eizo calibrated for Adobe RGB.
@ColinG
Did you try it with Preserve Color Details?? On my screen it makes difference, like yours.
George
I don’t get the unexpected shifts you noticed. Tested with DPL 7.1.1. on macOS Sonoma 14.1.2 on M1 MacBook Air 2020. Exported files get entries for sRGB in EXIF and MAKERNOTES too. Files checked with DPL7, LrC 12.5.1 and Finder’s QuickView as well as Preview.app. 
It does seem to help a little. I have changed my screen profile to P3 and that seems to be helping also. Thanks for testing @platypus. It still remains something of a mystery but as I say changing my display profile to Display P3 seems to have helped and not using the sharpener can also be of benefit.
Thank you for the help everybody 
If the sRGB profile is not embedded, this is the normal procedure: by default (according to the standard W3/ICC) ALL image files that do not have a profile are by definition sRGB.
Only files that have a profile other than sRGB must have the corresponding embedded profile.
If software opens a file without a profile [= sRGB] and assigns it another profile, it makes an error!
Many apps can be set to choose a WCS for files that have no info about what WCS they are supposed to be used with.
Imagine the primary colours r, g and b. Different WCS gamuts have those primaries in different places and the bigger the distance to white, the more saturation is possible. Absolute green is e.g. at 0,0,255 in the space that is used. In an other space, absolute green will be located closer to white or farther away and green will therefore appear with less or more saturation respectively.
Colin,
with your development / dop-file applied it is a completely different pic now.
Now as Softproof → sRGB was activated (as well → Advanced → Preserve color detail at default 50), I used the export function Same as Soft Proofing to create a new jpg-file in sRGB
and compared them …
with the viewer’s color management OFF
with the viewer’s color management ON
Colorwise I don’t see differences. So no problem here!
Colin; have you tried as George suggests ?
Set PCD = ON … 
This will instruct PL to protect colours that your sRGB screen is not capable of displaying. It might make the difference you’re looking for (?)
I have to wonder if “embed ICC profile - even when it’s sRGB” belongs in the Feature Requests section.
I haven’t run across this issue (Windows / IrfanView as viewer). Looking at my Irfan Settings / Color management, I have "enable color management set to display using my current monitor profile and "apply also for images without embedded color profile (slow!), set input ICC to [sRGB] - which probably explains why I don’t see an issue.
I just checked Feature Requests - there is a request to embed sRGB. I voted for it - maybe we all should?
In my experience there is no point in voting for a feature request because DxO just ignore them.
Might explain why it has less than 10 votes…
Cannot see any differences when exported to sRGB (with or without Preserve Color Details). Macbook Air M1, Sonoma 14.1.2, PL6 6.11.0. I suggest you check your ICC-files with the Colorsync utility and repair if needed.
Maybe @ColinG should give us the jpg too. See if there’s a difference between his jpg and our.
George
@ColinG
for (color) accuracy the raw-file needs to be viewed (compared) at 75% minimum
