The bread (made from processed wheat, probably bleached flour, and containing bread conditioners, preservatives) would almost surely fall into the ultra processed category, unless homemade from minimally processed whole wheat flour. The ham and cheese could as well, unless they were made with fairly traditional processes (and probably more expensive than what the typical person is buying at walmart, target, etc). They'd all probably be considered processed foods, at minimum.
I'd be surprised if commercially made ham didn't fall into the ultraprocessed category!
Saying this as someone who's curing his first ham in the fridge rn :-)
I run a chicken farm so I'm biased but for my family I grow out a bunch of birds to be bigger than typical (9-10lbs). Roast one of these and it sits in the fridge providing sandwich meat for a week, plus the occasional plate of hot sauce and cold meat. Super delicious and healthful.
My parents did this for most of my childhood. They weren't farmers, so the meat came from the supermarket – but larger cuts of meat (or whole chickens) are much cheaper than buying jointed, pre-cut or cooked meat anyway.