I'm not sure I can answer your question about whether the viral load reduces the more things you touch, and I can't guarantee that there wasn't virus on the outside of the beer, but probably you didn't get exposed unless you live in a super hotspot.
The thing to be worried about is getting the virus into your nose, throat, or eyes. The hands can move the virus to those places. The virus isn't dangerous to the skin on your hands, but to your respiratory system. If you touched something someone with Covid-19 had just that moment coughed on, and then absent-mindedly rubbed your eye or scratched your upper lip or wiped your nose, you could have passed live virus to a place on your body where you could breathe it in. But you would be more in danger if you were exposed to direct respiratory threats, like singing loudly in a choir and taking deep breaths between lines of the song, cheering at a crowded rally or football game, or sitting inside a restaurant with a lot of people who were all talking and laughing, and the restaurant had only one a/c unit that used recirculated air.
It's good to be cautious. I keep a spray bottle of hand sanitizer in my car, and some of those little clear gloves that cafeteria ladies use to hand you rolls and buns. But I don't always put them on, even when dropping in to a restaurant to get takeout. I do always put on my mask.
Try not to worry, it doesn't sound like you did yourself damage. Next time, just don't eat the chicken with your fingers. It's not sanitary for regular reasons (the hands pick up all kinds of bacteria) let alone safe nowadays.
The surface thing is so far theoretical, in that as far as I nobody who was contact traced had only had contact with a surface but had also been in close contact with someone who was breathing on them. It's wise to take all suggested precautions, so do wash your hands after touching something, but don't live in fear about it. Be very aware of who you're close to, though, and whether they are wearing a mask or not. There is a difference between being in, say, a covid serving hospital where viral load is constant and high or a school where again the percentage of infected people is very high although the disease isn't usually severe, and just touching something in a store. Peace.