According to Aurelien perceptual and relative intents don’t work in DT… I think you need lut based profiles for these to work but I am not sure… I just presented that diagram to emphasize the gamut being displayed by the two different indicators in DT…
EDIT:
I was on my phone before but I can see the difference now on my PC so something appears to be working here by choosing different intents…
EDIT2…
I can’t replicate what you were able to produce
With my xmp or the one you used and all combinations of settings LittleCMS off or on… setting intent with output profile and leaving export to image settings or at the export or setting both the to match I get the identical image with no observable difference between relative and perceptual. I wonder what others would see trying the same…
Edit3
Looking at the exif data my jpg are both rendered as perceptual despite having different settings applied… I wonder if my OS is doing something here…
But looking back I think I am seeing what others have so maybe I misunderstand what profiles you are using because I dont think the websafe one in DT will support intents… Colour management - intents