My sister was the canning queen and she made a lot of salsas, chutneys and things like bbq sauce (kind of a "meal starter/ convenience food" concept) as well as dilly beans and okra (which are pickled) and a variety of fruit preserves like marmalade, peach butter, and strawberry vanilla preserves. I typically lacto-ferment my pickles (or make quick fridge pickles) so I don't can them but I do like whole fig preserves, blackberry jelly, and plum sauce.
Non pickled vegetables are trickier to can since they are lower acid, except for tomatoes (which I would can if I had access to good ones in large quantities), and since I don't have a pressure canner, I do not can low acid foods. The aim of canning is to preserve food in an environment that is hostile to pathogens; sugar and acid, along with an anaerobic atmosphere (created by removing oxygen from the jars in a water bath or pressure canner) make the foods unlikely to grow pathogens and the process of canning is there to kill potential pathogenic bacteria that may have slipped in. So while I am maybe more chill about canning that some, I try to keep the basic chemistry in mind to keep the food preserved and safe.
So besides the canning to remove oxygen and kill bacteria, you need either an acidic environment or a sugary environment. There are a lot of lower sugar types of foods, but you can only go so low before the chemistry gets a little iffy for preservation. And if vinegar isn't your thing (and you don't follow the FDA's canning guidelines to the letter) the Italian method of preserving vegetables under oil, called "sottoli," (usually after somewhat dehydrating them) to keep out oxygen. There are some really intriguing treatments of zucchini, eggplant, and
mushrooms, peppers, and artichokes using this method. But it is at your own risk and not necessarily what most Americans think of as "canning."