Honours lists make no distinction between the FA Cup and the EFL Cup, but they do separate the super cups.
The Europa League (and now the Conference League) will still class as "major" honours even if they're less significant than winning the Champions League.
We all know that the Premier League and Champions League are the measure of the best managers, that goes without saying, but we've still got posters salivating over Mourinho's time at the club while slagging off Ten Hag for winning literally one of the same competitions, and that's basically the issue I have with the desperation from a specific set of posters to write off winning the EFL Cup as a "mickey mouse" achievement.