Work 870 have stock safety. Safety on top of trigger finger on safety, disengage as you mount the gun. That’s how I was trained at both academies I’ve been through. When I dismount I break my grip and put it back on. My personal 870 has the Wilson safety, I can use the side of my trigger finger to disengage it, much more ergonomic for me. I do the exact same thing on my 1301C for 3 gun stuff.
The only shotgun use I have is in the house as a stationary, not searching weapon. The gun is slide back, shell on elevator, safety off.
If I were to take the shotgun to go searching, I wouldn't use the safety, because the gun lacks a sling. So if I had to put it down, I'm going to run the pump to eject my live round and then roll it over and dump the round off the elevator out too. I won't go so far as to finish emptying the tube, but that would render it safe for sitting it down.
Still, I switched a rifle for this role and one reason I picked the Sig Rattler/MCX is that it has a firing pin block safety, making it drop safe. Allowing me to forego "cruiser ready" and worry far less about drop safety.