Data point for AF:

Gf who has Premium status was unable to add the number through KLM's website (even SAS app doesn't show ITA anymore), she used the support chat who confirmed it had been added, but couldn't see it reflected on the website under manage my booking. At CDG, SkyPriority lane dragon denied her access, claiming ITA was no longer in SkyTeam and that all benefits were gone. After some convincing, she was let through, check-in agent was unable to see the Volare number nor add it to the reservation. They did however let her check a free bag despite traveling on a Light fare, which I guess means that the CI agent was at least aware of some benefits continuing to be offered.

Upon trying to enter the lounge, an agent was able to have the number added to the reservation and lounge access was granted.

Curious to see how it'll go on the return from BCN in a week and whether these flights will be credited to Volare or FlyingBlue...