Welcome @ajmac25
It’s a good question, but applications don’t share cookies and haven’t for a very long time.
You can sign in to OpenAI via a bookmark in DEVONthink to set a per-application cookie for it and ask your questions just as you would in a browser.
And… drum roll, please 
*, if you clip as a formatted note, it looks and appears as you see it in the browser 
(And yes, I validated it behaved as expected with my network disabled!)