Good article. Basically, actors are not expected to check guns. It should have been done by the armorer and in this case also by AD who declared the gun to be "cold."
"Added Corrie: “The reason that Alec Baldwin did not check the firearm is because… he’s not given time to do so. It is an understood that when the firearm is handed to him it is in proper working order. And that is the responsibility of the armorer prop master, whoever is in control of the firearms on set. So all the armchair quarterbacks that are sitting back and saying well, Alec Baldwin is responsible because he didn’t check the gun, that’s not the procedure that’s used on set — so stop with that. Ultimately it is the responsibility of the armorer or prop master or whomever is on set in control and responsible for those firearms being available and made ready for each scene.”"
'Rust': Armorers and Propmasters Talk On-Set Gun Safety, What Happened - Variety