The language in the second email sounds more limited to me:

"Your new Citi benefits will be available starting April 24, 2026, and you can keep enjoying the Barclays benefits you love for a limited period of time. To take advantage of these benefits, continue using your AAdvantage® Aviator® credit card until you receive and activate your new Citi credit card" (emphasis added)

Could be read in different ways, but I am going to plan to use the Barclays' benefits before I activate the Citi replacement card.