P: Lightroom Classic: Editing raw file in PS from LR loses profile

@andrew_rodney I exported the dng from LrC just to do the test you asked me to do.  I had previously set the Color Settings to "ask" in case there were issues related to this troubleshooting.  Normally, I have them on "preserve" as you suggest.  The dng is 79MB.  I can try to upload it somewhere if you think there is value to that.  The dng did open in ACR as you say.  I didn't mention that because that is normal behavior.

Set color policies to PRESERVE then you will not get that dialog and the embedded profile will be honored. See:

Photoshop CC's Color Settings & the Convert to Profile and Assign Profile command.

This new video covers everything you thought you wanted to know about the Photoshop Color Setting dialog. It also discusses the Convert to Profile Command and the Assign Profile Command. Photoshop CC 2017 is used in this video and it updates the video on this subject I Published on June 28, 2012.

High Rez: http://digitaldog.net/files/PhotoshopColorSettings.mp4
Low Rez (YouTube): https://www.youtube.com/watch?v=6JaHOGDK5OI

Also, a DNG should open in ACR if indeed it's raw. It would never have Adobe RGB (1998) as an embedded profile. What and where did that DNG come from and can you upload it?

@andrew_rodney I tried that and unsurprisingly that worked.  However, when I opened the dng, I got a warning message below.  Is that a clue??  In the other attached image below, left is LR, you can see the profile applied in the develop module.  Right side is PS with the .cr3 file "Open for Editing in PhotoShop 2021" and the dng file opened directly from PS.  You can clearly see the profile is not applied in PS for the .cr3 and it is for the .dng.

You are correct.

I also burnt a line and it carried over, along with a dramatic exposure change. My workflow with this album required me to only change colour and lens profiles before "Edit in Photohshop"

Also...
Manually adding Ps as an "Edit in" program doesn't carry the colour profile across either.
Other software works as expected (I tried with Luminar 4 and Nik Collection)

@koketso Do you really lose all edits?  I thought that at one point too, but to convince myself I was only losing the color profile, I used the adjustment brush to burn a line right across the image before "Edit in Photoshop" and the burn was still there (although due to the loss of the color profile, the image otherwise looked very different).

Can also confirm that this behaviour only happens with .CR3 files.
I lose all LrC edits when "Edit in Photoshop".

Best to export as DNG then profile is wrapped inside with XMP. 

@andrew_rodney Hi.  I'm happy to upload the image.  In fact I sent one to @arjun_haarith in email, along with the .xmp.  The profile I purchased so I'm hesitant to send that without getting permission from the person who created it.  Why don't you buy it from Color Fidelity.  it is only $15.  if you would like me to upload another image, please give me instructions exactly what you would like and I'll do that.  I really do appreciate your help!

*neodes24 Exactly - I'm pretty sure it is not a problem with my computer or settings or anything like that.  It has to be ACR component in PS.  All things point to that so far.

So it would be useful to take such a raw and suspect profile, export as DNG, upload so we could see how it behaves in LR/ACR/Photoshop.