When I recently got a new passport, I made a point to be sure to use an airport kiosk to check in for my next international flight. That is the ONLY way that my passport gets the "Verified" flag in my Delta profile. "Supposedly" it is also possible to use the Delta app to do this - never worked for me. I've only had success using an airport kiosk to do this.

To be clear, as mentioned several times in this thread, having a Delta agent scan your passport gets your passport verified - for THAT FLIGHT ONLY. A Delta agent's passport scan does NOT update your Delta profile with the "Verified" flag.

OP should use a kiosk to check in for their next international flight. That will set that passport in their profile as "Verified" and it should stick for the life of that passport. When a traveler's passport is "Verified" by Delta in their profile, Delta will issue DOCS OK boarding passes for future international flights to destinations where Delta doesn't also have to verify other travel requirements (such as visas).