Hi,
That interaction was ruled against almost three years ago:
Cosmo (Star-Lord, 20/Nebula, 20) was originally written to allow him to interact with any deck in the game. Many players have found him an invaluable companion for Doctor Strange and his invocation deck. However, we have found over time that this flexibility creates obstacles when we are trying to design scenarios or heroes who have a special deck that would be negatively affected by Cosmo’s ability. For that reason, we have decided to restrict Cosmo’s ability to only affecting player decks and the encounter deck, which still provides him a great deal of flexibility without standing in the way of new designs.
Taken from here: https://www.fantasyflightgames.com/en/news/2023/5/18/rules-reference-debrief-1/