I have a really old vest (Gander mountain) that has a recoil pad pocket. I can put either a Browning impact gel pad in there or a recoil pad. I'm sure somebody makes a similar vest now.
My shotgun is an 1100 Remington semi auto twelve, I usually use either 2 or 4 semi magnum 2 3/4, 2 shot for Hare, Geese or Fox, 4 for everything else.. With the recoil stock extension on my shotgun, the spring type recoil system of the Remington (or similar) and the impact gel vest, felt recoil is negligible.
Not all semi auto shotguns are designed the same, the ones with the recoil spring in the stock have less felt recoil than those without.
My days of shooting firearms, that kill in front and cripple behind, are long gone. I haven't come home with a sore shoulder, after a Dove hunt, in decades. I say Dove hunt because I limit out on Dove most every hunt. The guys that use a 20 gauge seem to get just as many birds as anybody else, those using three inch magnums don't seem to get any more.