There are a good few options for tinned beans of various sorts in the US.
There are also a good few options when it comes to sausages.
'Breakfast sausages' are probably the closest to traditional British sausages, but they are mainly eaten at breakfast. You'd have them with fried or scrambled eggs, maybe bacon, maybe pancakes or waffles, and syrup. Possibly ketchup.
Other sausages include Mexican style chorizo, which crumbles on the pan. Usually served with eggs, probably wrapped in a tortilla, with salsa, for breakfast.
There is also bratwurst, both Polish and German style, normally served on a long bun with mustard or ketchup, fried onions, maybe dill relish.
Also Italian sausage, frequently served on a long bun, with fried peppers and onions and kept warm in pepper and onion juices, and often dipped in the juices or with the juices ladled over to serve.
I live in a city that runs on sausages and has its own famous style of serving hotdogs with NO KETCHUP.
People don't really serve mashed potatoes as a weekday quick meal for kids. It's more likely to be oven fries or frozen pizza. So the bangers and mash issue wouldn't arise. Sausages are more likely to go in a gumbo or rice dish - Zatarains black beans and rice or other rice and quick cook packs suggest adding some kind of smoked sausage or other meat to the mix. There are a lot of precooked sausages available - Hillshire Farm sells various smoked pork, beef, and turkey sausage where I live. You can put them on the grill or slice and saute.
Sausages are often grilled and are a popular BBQ option.
For beans:
The closest to British beans is probably Boston baked beans. These take quite a lot of cooking. You can buy them tinned.
There is red beans and rice - especially Popeyes red beans and rice, a Louisiana dish. Can be made at home but easier to buy from Popeyes and they are lush. Eaten with fried chicken.
There are refried black beans and pinto beans, usually served with Tex-Mex meals. You can get them in various styles - authentic, fat free, spiced with chili powder, cumin...
Pork and beans is baked beans with pork chunks, slightly sweet with BBQ flavour.
Black beans, cannelini beans, garbanzo beans kidney beans - would all go into either a salad or chili or curry. Basically these are unflavored beans that come in a can.
There are also dried lentils and beans.
If you wanted to have a specific style of beans.
There's a range of beans of various flavours called Bush's Sidekicks - Taco Fiesta, Southwest Zest, Rustic Tuscany, Simmering Caribbean (geddit?)..
I buy chili beans in Aldi - 'mild' chili beans that come in a tin with a sauce that's quite spicy.