The next Call of Duty has been leaked and it is named Call of Duty Black Ops Cold War. The full trailer is coming August 26. No platforms have been announced for the game at present so hopefully, Stadia will be mentioned. Activision is releasing Sekiro onto Stadia so Activision will have a presence on Stadia in the coming weeks.
Also, Activision signed in a massive deal with YouTube to stream eSports. With one features of Stadia being Click to Play it would make sense that Call of Duty came to Stadia. Again are no platforms mentioned and this speculation.
This was discovered by Call of Duty News